It should be possible to set the email notifications so that if a ticket is assigned to a specific user in a group an email doesn't go to the whole group, but if a ticket is assigned to a group and not a specific user, then the whole group is notified.
For example, I am a member of the helpdesk group. If a ticket is assigned to me within the helpdesk group, I can get 2 emails (one for group assignment, one for personal assignment,) and everyone else in the helpdesk group gets an email as well. This doesn't make sense, since the ticket has been assigned to an individual, the whole group doesn't need notification. However, if I turn off group notification, then no one will be notified if a ticket is assigned to the group, but not an individual agent.