Is having a sub menu possible in Android?
And what do you call this view in Android?
As others have mentioned, this is an ExpandableListView, within a NavigationDrawer. There are several tutorials you can use (see my list below).
ExpandableListView
NavigationDrawer
One piece of advice based on personal experience: the baseline behavior for the SimpleExpandableListAdapter is pretty limiting and often not what you're looking for in your customization. If you're looking to have your own specific behavior and look-and-feel to the sub menus, I highly recommend looking into extending the BaseExpandableListAdapter yourself and creating your own custom adapter. [This may seem daunting at first, but it's not terribly hard once you have a grasp on your parents and children within your menu and sub menu(s).]
SimpleExpandableListAdapter
BaseExpandableListAdapter
ExpandableListAdapter
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