HOWTO: Enable Limited Administrator the right to Move Groups

Hello,

I am trying to delegate the task of moving hundreds of groups into several groups in SEPM (version 12 RU2)

So far, our Techs have been assigned Limited Administrator right, and they can access the groups they are supposed to move, but when they right-click, Move is greyed out, even though the group is not inheriting from any other group.

Here is a screenshot of the Limited Administrator policy

What other rights can I assign to these Limited Administrators so they can move one group into another, without giving them more rights than necessary?