You will need the Full Write Groups permission to preform this task.
How to set the Hierarchy of a group
When adding a new group, there is a tab named "Hierarchy" where you can indicate a parent group as well as one or more child groups (a.k.a. subgroups).
New Group > Hierarchy Tab
Note: By setting a parent group you automatically make the current group a subgroup.
After you have set the Parent group. you can also add subgroups from this Hierarchy Screen for your group.
Note: Group Admins of parent groups can access to all subgroup information
How do I edit a Hierarchy of a group
When editing a group, there is a tab named "Hierarchy" where you can indicate a parent group as well as one or more child groups (a.k.a. subgroups).
Open the group > Select Edit group from the top right Actions Dropdown > Then select the hierarchy tab.
After you have selected the Hierarchy tab, you can set the Parent group by trying in the name of the Group next to the Parent section.
Note: By setting a parent group you automatically make the current group a subgroup.
After you have set the Parent group. you can also add subgroups from this Hierarchy Screen for your group.
Note: Group Admins of parent groups can access to all subgroup information