Person groups and their settings can be found in: Worktime > Administration > Person groups. A person group can be moved by selecting 'Move person group' from the Action menu.
Choose the person group you want to move.
Select new parent group.
Then press 'Move'.
Making a child group into a parent group
This is how to change a child group into a parent group:
Choose the person group you want to move.
Select 'Move person group' from the Action menu.
Select the top empty row as 'New parent group'.
The former child group now has no parent group and therefore becomes one itself.