Thanks for great support!
I turned off one by one and came down to the very last “WP Native Dashboard 1.3.12”, which solved the problem. I have been developing in Instant WordPress locally and by default that plugin is installed. Now that I have moved to live that plugin followed along. I am not sure what it really do (possible benefits) as its 1. Very old 2. The features it contain perhaps are already included in later releases of WP.
In any case it seems to have solved my problem and I will continue to configure Private groups =)
Thanks again for your help! (y)