Go to My Groups >> Admin >> Preferences >> New Submissions.

By default you have a row for Group Admins, and a row for Group Members. Also you will se a row for any of the subgroups you may have already created in the system. (for instructions on creating and managing Subgroups please Click Here).

In the first column, you choose which subgroups should have access to all New Submissions. In the second column you choose which subgroups should receive the New Submission Notifications.