diff --git a/moto/elbv2/exceptions.py b/moto/elbv2/exceptions.py
index 9550fcb9e..dd2fa6ee9 100644
--- a/moto/elbv2/exceptions.py
+++ b/moto/elbv2/exceptions.py
@@ -35,9 +35,7 @@ class SubnetNotFoundError(ELBClientError):
 
 class TargetGroupNotFoundError(ELBClientError):
     def __init__(self) -> None:
-        super().__init__(
-            "TargetGroupNotFound", "The specified target group does not exist."
-        )
+        super().__init__("TargetGroupNotFound", "One or more target groups not found")
 
 
 class TooManyTagsError(ELBClientError):
diff --git a/moto/elbv2/models.py b/moto/elbv2/models.py
index 9f0e53e2d..2ae4f3f51 100644
--- a/moto/elbv2/models.py
+++ b/moto/elbv2/models.py
@@ -1377,20 +1377,33 @@ Member must satisfy regular expression pattern: {expression}"
         target_group_arns: List[str],
         names: Optional[List[str]],
     ) -> Iterable[FakeTargetGroup]:
+
+        args = sum(bool(arg) for arg in [load_balancer_arn, target_group_arns, names])
+
+        if args > 1:
+            raise ValidationError(
+                "Target group names, target group ARNs, and a load balancer ARN cannot be specified at the same time"
+            )
+
         if load_balancer_arn:
             if load_balancer_arn not in self.load_balancers:
                 raise LoadBalancerNotFoundError()
-            return [
+            target_groups = [
                 tg
                 for tg in self.target_groups.values()
                 if load_balancer_arn in tg.load_balancer_arns
             ]
+            if target_groups is None or len(target_groups) == 0:
+                raise TargetGroupNotFoundError()
+            return sorted(target_groups, key=lambda tg: tg.name)
 
         if target_group_arns:
             try:
-                return [self.target_groups[arn] for arn in target_group_arns]
+                target_groups = [self.target_groups[arn] for arn in target_group_arns]
+                return sorted(target_groups, key=lambda tg: tg.name)
             except KeyError:
                 raise TargetGroupNotFoundError()
+
         if names:
             matched = []
             for name in names:
@@ -1401,9 +1414,9 @@ Member must satisfy regular expression pattern: {expression}"
                 if not found:
                     raise TargetGroupNotFoundError()
                 matched.append(found)
-            return matched
+            return sorted(matched, key=lambda tg: tg.name)
 
-        return self.target_groups.values()
+        return sorted(self.target_groups.values(), key=lambda tg: tg.name)
 
     def describe_listeners(
         self, load_balancer_arn: Optional[str], listener_arns: List[str]
diff --git a/moto/elbv2/responses.py b/moto/elbv2/responses.py
index 652d5b9b9..443d92fbb 100644
--- a/moto/elbv2/responses.py
+++ b/moto/elbv2/responses.py
@@ -1070,6 +1070,7 @@ DESCRIBE_TARGET_GROUPS_TEMPLATE = """<DescribeTargetGroupsResponse xmlns="http:/
         {% if target_group.vpc_id %}
         <VpcId>{{ target_group.vpc_id }}</VpcId>
         {% endif %}
+        <IpAddressType>{{ target_group.ip_address_type }}</IpAddressType>
         <HealthCheckProtocol>{{ target_group.healthcheck_protocol }}</HealthCheckProtocol>
         {% if target_group.healthcheck_port %}<HealthCheckPort>{{ target_group.healthcheck_port }}</HealthCheckPort>{% endif %}
         <HealthCheckPath>{{ target_group.healthcheck_path or '' }}</HealthCheckPath>
diff --git a/tests/test_elbv2/test_elbv2_target_groups.py b/tests/test_elbv2/test_elbv2_target_groups.py
index 53e311e11..1370cb8fe 100644
--- a/tests/test_elbv2/test_elbv2_target_groups.py
+++ b/tests/test_elbv2/test_elbv2_target_groups.py
@@ -122,7 +122,7 @@ def test_create_target_group_and_listeners():
     http_listener_arn = listener["ListenerArn"]
 
     response = conn.describe_target_groups(
-        LoadBalancerArn=load_balancer_arn, Names=["a-target"]
+        LoadBalancerArn=load_balancer_arn,
     )
     assert len(response["TargetGroups"]) == 1
 
@@ -455,17 +455,23 @@ def test_describe_invalid_target_group():
         conn.describe_target_groups(Names=["invalid"])
     err = exc.value.response["Error"]
     assert err["Code"] == "TargetGroupNotFound"
-    assert err["Message"] == "The specified target group does not exist."
+    assert err["Message"] == "One or more target groups not found"
 
 
 @mock_elbv2
 @mock_ec2
-def test_describe_target_groups_no_arguments():
+def test_describe_target_groups():
+    elbv2 = boto3.client("elbv2", region_name="us-east-1")
+
     response, vpc, _, _, _, conn = create_load_balancer()
 
+    lb_arn = response["LoadBalancers"][0]["LoadBalancerArn"]
     assert "LoadBalancerArn" in response["LoadBalancers"][0]
 
-    conn.create_target_group(
+    groups = conn.describe_target_groups()["TargetGroups"]
+    assert len(groups) == 0
+
+    response = conn.create_target_group(
         Name="a-target",
         Protocol="HTTP",
         Port=8080,
@@ -479,11 +485,84 @@ def test_describe_target_groups_no_arguments():
         UnhealthyThresholdCount=2,
         Matcher={"HttpCode": "201"},
     )
+    arn_a = response["TargetGroups"][0]["TargetGroupArn"]
+
+    conn.create_listener(
+        LoadBalancerArn=lb_arn,
+        Protocol="HTTP",
+        Port=80,
+        DefaultActions=[{"Type": "forward", "TargetGroupArn": arn_a}],
+    )
 
     groups = conn.describe_target_groups()["TargetGroups"]
     assert len(groups) == 1
     assert groups[0]["Matcher"] == {"HttpCode": "201"}
 
+    response = elbv2.create_target_group(
+        Name="c-target",
+        Protocol="HTTP",
+        Port=8081,
+        VpcId=vpc.id,
+    )
+    arn_c = response["TargetGroups"][0]["TargetGroupArn"]
+    groups = conn.describe_target_groups()["TargetGroups"]
+    assert len(groups) == 2
+    assert groups[0]["TargetGroupName"] == "a-target"
+    assert groups[1]["TargetGroupName"] == "c-target"
+
+    response = elbv2.create_target_group(
+        Name="b-target",
+        Protocol="HTTP",
+        Port=8082,
+        VpcId=vpc.id,
+    )
+    arn_b = response["TargetGroups"][0]["TargetGroupArn"]
+    groups = conn.describe_target_groups()["TargetGroups"]
+    assert len(groups) == 3
+    assert groups[0]["TargetGroupName"] == "a-target"
+    assert groups[1]["TargetGroupName"] == "b-target"
+    assert groups[2]["TargetGroupName"] == "c-target"
+
+    groups = conn.describe_target_groups(Names=["a-target"])["TargetGroups"]
+    assert len(groups) == 1
+    assert groups[0]["TargetGroupName"] == "a-target"
+
+    groups = conn.describe_target_groups(Names=["a-target", "b-target"])["TargetGroups"]
+    assert len(groups) == 2
+    assert groups[0]["TargetGroupName"] == "a-target"
+    assert groups[1]["TargetGroupName"] == "b-target"
+
+    groups = conn.describe_target_groups(TargetGroupArns=[arn_b])["TargetGroups"]
+    assert len(groups) == 1
+    assert groups[0]["TargetGroupName"] == "b-target"
+
+    groups = conn.describe_target_groups(TargetGroupArns=[arn_b, arn_c])["TargetGroups"]
+    assert len(groups) == 2
+    assert groups[0]["TargetGroupName"] == "b-target"
+    assert groups[1]["TargetGroupName"] == "c-target"
+
+    groups = conn.describe_target_groups(LoadBalancerArn=lb_arn)["TargetGroups"]
+    assert len(groups) == 1
+    assert groups[0]["TargetGroupName"] == "a-target"
+
+    response = conn.create_target_group(
+        Name="d-target",
+        Protocol="HTTP",
+        Port=8082,
+        VpcId=vpc.id,
+    )
+    arn_d = response["TargetGroups"][0]["TargetGroupArn"]
+    conn.create_listener(
+        LoadBalancerArn=lb_arn,
+        Protocol="HTTP",
+        Port=80,
+        DefaultActions=[{"Type": "forward", "TargetGroupArn": arn_d}],
+    )
+    groups = conn.describe_target_groups(LoadBalancerArn=lb_arn)["TargetGroups"]
+    assert len(groups) == 2
+    assert groups[0]["TargetGroupName"] == "a-target"
+    assert groups[1]["TargetGroupName"] == "d-target"
+
 
 @mock_elbv2
 @mock_ec2