Hello,
we were writing via e-mails but for other visitors:
1. You can create a custom field for groups in 
Site manager -> Development -> System tables -> Group. You can for example develop a department selector 
form control and assign each group to a department. Then you can use a Where condition about this property when you display the groups under the department.
2. You can use the 
Group pages location property of Groups and then use it in the Where condition when you display the groups. Group pages location can contain the path of the proper department, for example:
Group 1 of Department 1:
Group pages location: /department1/group1You can add the State property like mentioned above in  
Site manager -> Development -> System tables -> Group.
Best regards,
Helena Grulichova