Google Group Memberships can be changed by the Owner or Manager of the Group: Managing Members to a Google Group
When a Group is created, an owner/Manager is/are designated. It is recommended for at least 2 people to hold the role of Owner.
For most Groups, there is no difference between Owner and Manager. Using Owner is advised when special granular permissions are not a part of the Group Design.
If your Department has lost control over the Group (eg both Owners left the College at the same time without transferring control of the Group to a successor), please open a ticket to request that a new Owner be designated. That Owner should then assign a 2nd, as well as modify any additional Memberships.
It is recommended to audit the list of existing Members/Owners regularly to ensure proper access.