diff --git a/cosmos/airflow/graph.py b/cosmos/airflow/graph.py
index eaf732bfa..9de21292e 100644
--- a/cosmos/airflow/graph.py
+++ b/cosmos/airflow/graph.py
@@ -259,6 +259,7 @@ def _add_dbt_compile_task(
     execution_mode: ExecutionMode,
     task_args: dict[str, Any],
     tasks_map: dict[str, Any],
+    task_group: TaskGroup | None,
 ) -> None:
     if execution_mode != ExecutionMode.AIRFLOW_ASYNC:
         return
@@ -269,7 +270,7 @@ def _add_dbt_compile_task(
         arguments=task_args,
         extra_context={},
     )
-    compile_airflow_task = create_airflow_task(compile_task_metadata, dag, task_group=None)
+    compile_airflow_task = create_airflow_task(compile_task_metadata, dag, task_group=task_group)
     tasks_map[DBT_COMPILE_TASK_ID] = compile_airflow_task
 
     for node_id, node in nodes.items():
@@ -357,7 +358,7 @@ def build_airflow_graph(
         for leaf_node_id in leaves_ids:
             tasks_map[leaf_node_id] >> test_task
 
-    _add_dbt_compile_task(nodes, dag, execution_mode, task_args, tasks_map)
+    _add_dbt_compile_task(nodes, dag, execution_mode, task_args, tasks_map, task_group)
 
     create_airflow_task_dependencies(nodes, tasks_map)
 
diff --git a/cosmos/operators/local.py b/cosmos/operators/local.py
index 8cda2f883..8bbee1a44 100644
--- a/cosmos/operators/local.py
+++ b/cosmos/operators/local.py
@@ -310,6 +310,28 @@ def _configure_remote_target_path() -> tuple[Path, str] | tuple[None, None]:
 
         return _configured_target_path, remote_conn_id
 
+    def _construct_dest_file_path(
+        self, dest_target_dir: Path, file_path: str, source_compiled_dir: Path, context: Context
+    ) -> str:
+        """
+        Construct the destination path for the compiled SQL files to be uploaded to the remote store.
+        """
+        dest_target_dir_str = str(dest_target_dir).rstrip("/")
+
+        task = context["task"]
+        dag_id = task.dag_id
+        task_group_id = task.task_group.group_id if task.task_group else None
+        identifiers_list = []
+        if dag_id:
+            identifiers_list.append(dag_id)
+        if task_group_id:
+            identifiers_list.append(task_group_id)
+        dag_task_group_identifier = "__".join(identifiers_list)
+
+        rel_path = os.path.relpath(file_path, source_compiled_dir).lstrip("/")
+
+        return f"{dest_target_dir_str}/{dag_task_group_identifier}/compiled/{rel_path}"
+
     def upload_compiled_sql(self, tmp_project_dir: str, context: Context) -> None:
         """
         Uploads the compiled SQL files from the dbt compile output to the remote store.
@@ -327,16 +349,11 @@ def upload_compiled_sql(self, tmp_project_dir: str, context: Context) -> None:
 
         source_compiled_dir = Path(tmp_project_dir) / "target" / "compiled"
         files = [str(file) for file in source_compiled_dir.rglob("*") if file.is_file()]
-
         for file_path in files:
-            rel_path = os.path.relpath(file_path, source_compiled_dir)
-
-            dest_path = ObjectStoragePath(
-                f"{str(dest_target_dir).rstrip('/')}/{context['dag'].dag_id}/{rel_path.lstrip('/')}",
-                conn_id=dest_conn_id,
-            )
-            ObjectStoragePath(file_path).copy(dest_path)
-            self.log.debug("Copied %s to %s", file_path, dest_path)
+            dest_file_path = self._construct_dest_file_path(dest_target_dir, file_path, source_compiled_dir, context)
+            dest_object_storage_path = ObjectStoragePath(dest_file_path, conn_id=dest_conn_id)
+            ObjectStoragePath(file_path).copy(dest_object_storage_path)
+            self.log.debug("Copied %s to %s", file_path, dest_object_storage_path)
 
     @provide_session
     def store_freshness_json(self, tmp_project_dir: str, context: Context, session: Session = NEW_SESSION) -> None:
diff --git a/tests/operators/test_local.py b/tests/operators/test_local.py
index a6e7f2caa..c7615225f 100644
--- a/tests/operators/test_local.py
+++ b/tests/operators/test_local.py
@@ -1241,6 +1241,7 @@ def test_upload_compiled_sql_should_upload(mock_configure_remote, mock_object_st
         task_id="fake-task",
         profile_config=profile_config,
         project_dir="fake-dir",
+        dag=DAG("test_dag", start_date=datetime(2024, 4, 16)),
     )
 
     mock_configure_remote.return_value = ("mock_remote_path", "mock_conn_id")
@@ -1259,12 +1260,10 @@ def test_upload_compiled_sql_should_upload(mock_configure_remote, mock_object_st
     files = [file1, file2]
 
     with patch.object(Path, "rglob", return_value=files):
-        context = {"dag": MagicMock(dag_id="test_dag")}
-
-        operator.upload_compiled_sql(tmp_project_dir, context)
+        operator.upload_compiled_sql(tmp_project_dir, context={"task": operator})
 
         for file_path in files:
             rel_path = os.path.relpath(str(file_path), str(source_compiled_dir))
-            expected_dest_path = f"mock_remote_path/test_dag/{rel_path.lstrip('/')}"
+            expected_dest_path = f"mock_remote_path/test_dag/compiled/{rel_path.lstrip('/')}"
             mock_object_storage_path.assert_any_call(expected_dest_path, conn_id="mock_conn_id")
             mock_object_storage_path.return_value.copy.assert_any_call(mock_object_storage_path.return_value)