The order of the groups within Workspace can be changed. A user can only change the order of their personal groups. An admin can change the order of shared groups.

As a user, click “Edit your workspace”. Or right click on a tile. On the top of a group the drag handle appears. To change the order, drag and drop the group to the desired location.

If you like to change the default order for Shared Groups as an admin, click "Groups".

Here you can change the default order for the shared groups by moving the groups in the desired position.