Group owners cannot see group if "Group is visible to all users" is off

Ok. So your requirement would be:

  • show non-public groups on the group page (but only to group members)

To cover the scenario of not showing public groups, how about also:

  • add setting to individual group page for hide on group page

Groups can be used for a lot of different reasons (permissions, events, directories, badges, etc.) so suppressing a group from the /groups page would be a nice option to have.