This feature request affects environments with user plus (end user group selector) and has been discussed as a possibility with the Figshare developers, but requires further consideration from the Product Team, which is why I'm listing it as a feature request.
When the group selector is enabled for end users, users can see all groups on the portal underneath the group that they are associated with. This includes both public and private groups.
However, admins of a number of FFI portals have expressed the need for private groups NOT to be visible on the group selector for end users (but only available on the admin group selector).
The solution would be to add a flag (in the group settings) for the admin to set whether a group should be selectable for end users or admins. In this way, an admin could create a private group, and choose to make it display on the group selector or not.
Thanks Kay for adding this, I did however notice that I added the same request a couple of months ago - but your explanation for the feature request sounds clearer: