Want to know how to have email notification to only go to specific groups and not to all agents

You can group the agents you want the notification to go out and set up a Dispatch'r rule such that if a ticket with the conditions you choose is created, the notification is sent out to that group alone. Or if you want only the group to receive the notification when the ticket is assigned to it, then go to Admin > Email notifications > Agent notifications > Ticket Assigned to Group. And you can turn off the New ticket created notifications. Another option is to only specify the names of the agents under the New ticket created notification whom you wish to send out the notification to.