Hello, @Moin! 
Thanks for reporting this. We initially treated this as a bug, but it seems that this quirk is documented when setting up a group:
If the group itself is set to not be visible, it will not show up in the flair of its members.
I’m bringing this question back to the product team to see if we want to improve this somehow, as it is currently not possible to have a visible group with hidden members without leaking the membership through flair.
Will reply here when we have an update. 