I see that it is possible to list all members that belong to a specific group, as documented here:
https://developers.google.com/admin-sdk/directory/v1/guides/manage-group-members#get_all_members
But is it possible to get a list of groups that a user belongs to? I was hoping that Users.get would contain this information, or the Members API would have something similar, but I don't see it.
So I've found the solution in the Developer Guide, although it does not exist in the API documentation!!
https://developers.google.com/admin-sdk/directory/v1/guides/manage-groups#get_all_member_groups