According to https://developer.android.com/about/versions/android-4.2.html#NestedFragments, you can use nested fragments to achieve this by calling getChildFragmentManager() if you still want to use the Google Maps fragment instead of the view inside your own fragment:
SupportMapFragment mapFragment = new SupportMapFragment();
FragmentTransaction transaction = getChildFragmentManager().beginTransaction();
transaction.add(R.id.content, mapFragment).commit();
where "content" is the root layout in your fragment (preferably a FrameLayout). The advantage of using a map fragment is that then the map lifecycle is managed automatically by the system.
Although the documentation says "You cannot inflate a layout into a fragment when that layout includes a <fragment>. Nested fragments are only supported when added to a fragment dynamically. ", I have somehow successfully done this and it worked fine. Here is my code:
In the fragment's onCreateView() method:
View view = inflater.inflate(R.layout.layout_maps, container, false);
SupportMapFragment mapFragment = (SupportMapFragment) getChildFragmentManager().findFragmentById(R.id.map);
mapFragment.getMapAsync(...);
In the layout:
<fragment xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:tools="http://schemas.android.com/tools"
android:id="@+id/map"
android:name="com.google.android.gms.maps.SupportMapFragment"
android:layout_width="match_parent"
android:layout_height="match_parent" />
Hope it helps!