Thx for your answer Chris Andre may be a misunderstanding. The context settings in studio/settings/general are enabled.....

Conclusio: A group, set for a membership level, is not visible for that level in group-home and can only be found by group search. Please @LeonidS have a look at this....

Site Group Home (new groups):

• If ''visibility of a group by membership level'' is set, this group is NOT visible on the groups-home page.
• Neighter for the set membership level allowed to see this group nor anybody else (included group owner and site-admin)

Site group search:

• Group can be found by the membership level that is set, group owner and site admin.
• other levels just see a Private Group, that is OK

The group settings of this group :

• Visibility is set to a membership level
• Approval to join is enabled
• Post only Participants is enabled