I’ve thought up two ways to reorder the group list so their position remains fixed, mockups are below.
Because like Moin said different languages would move groups around if they were ordered by First Name.
Option 1:
The easiest option is drag categories around however if there are lots of categories this would easily become a cumbersome task.
On the /g groups page add a new button 
Reorder Groups
Then grip icons appear and you’d be able to drag groups around at your content. However, this is not that mobile friendly if there are lots of groups.
Option 2
Perhaps the way to approach this is by using existing UI to reorder groups. I took inspiration from the edit badge group and the category fixed positions editor.
Essentially, you’d create a group name for your groups, and be able to order them in any way you want and then you’d add groups into the group name you made and order them around too. Sorry that is confusing 
Again you’d start off with Reorder Groups button
That would bring up this group editor. So just like the badge editor where you can move around the Getting started, community & posting groups etc
You can then edit / reorganise the Region group for example like so by pressing the icon in the Group Editor (pictured above)
Thoughts?