Translations:Groups/56/en

|Those with the right permissions may invite new members to the group. |} The visibility of a group determines whether or not the group can be represented or displayed on a member's profile. This setting cannot be changed later.

Public	Members can choose to advertise the group on their profile.
Private	The group cannot be advertised or displayed by members.

As mentioned, any user can manually obscure of any public group from displaying on their profile via Visibility settings.