You can join a Group from the GlobaliD Mobile app or Web app.
Regardless of the type of Group, it's always optional whether you want to share your membership to a group publicly or remain hidden.
While joining, if you select to keep your membership hidden, you will still be a complete member of the Group but your membership will be hidden to others.
Similarly, a Group Owner can choose to have the entire membership list for a Group to be hidden, in order to protect the privacy of its members.
The Group Owner or Admin can change this in Group Settings on the Global.iD Web App.