Now a days few companies are using "Add To Update Set" utility from share.
If you use this then you can directly go to that specific group record and click on Add To Update Set, it will automatically capture all the necessary records and related records in update set.
Otherwise, if your company instance doesnt use it , then the process suggested above in other comments , is helpful . but i believe you might have to do additional things after that as well, for adding those members and roles.
