Add 'not in group' section to group overview page

On the page Course settings > Users > Group > Overview

At the the moment there are two overview sections 'groupings' and 'not in a grouping'.
But there's no hint who of the students are not in a group. They are not displayed.
Edit:
We would like to have a third section [not in a group] who displays the group 'no group'. In there, there should be all participants listed that are in no group.
Additionally, the grouping [not in a group] and the group [no group] should be selectable from the dropdown menus.
I attach a mockup (edited), so that it is more visible what I would like to have.