Google currently has many ways to create groups and different types of groups.
- Groups created by admin using Admin SDK or admin.google.com
- Groups created on groups.google.com
- Security Group created using Cloud Identity Groups API
- Dynamic Group created in admin.google.com
Depending on how the groups were created and the type of the group, what you can or cannot do as an admin may vary. I have done a preliminary testing and shared the file publicly for viewing.
If you have different experience, or if I missed anything, please leave a comment below.