In order to be able to manage Groups and Group membership you must have been assigned the following permissions : Manage Groups & Permissions
Manage Groups & Permissions are part of the Post Management Permissions/Personnel Permissions - see Screenshot below :
Note : once you have been assigned the Manage Groups & Permissions you are able to create Groups (Service Provider groups) and Permissions and Users to these Groups. Typically these permissions will be assigned to a Post Administrator.
As of release v1.25.0, the "Manage Permissions" page has been split into two pages, one for managing Service Providers and the other for managing Service Provider Groups. The new "Manage Service Providers" page displays all users with Service Provider permissions to the organization. Service Providers can easily have their permissions removed from here too. The new "Manage Service Provider Groups" page functions very similar to the old user interface, just as its own dedicated page now.