1/ create a group A
2/ give edit right to another user or to another group on the document of group A. The purpose of this is to allow users which are not administrators to manage some groups. Make sure that this user is not admin, and that he cannot delete the group page
3/ login with the user from step 2 or a user from the group from step 2
4/ go on the group A page, click on the edit button (which will be visible)
5/ the group edit form will display properly, allowing the user to add new users or subgroups in group A. However *the remove button in the table will not be displayed* - see screenshot
This prevents the user from actually managing the group properly.
I investigated a bit and noticed that this is because, when displaying the actions column of that table in edit mode, we're actually checking delete rights on the groups page, not edit rights on the group, which explains why this works fine for administrators.