Organization Owners have full rights to Notifications Admin. They can set permissions, manage settings, and manage all lists and subscribers. Groups set in Staff Portal can also be assigned permissions, however, the users of these Groups may only manage all lists and subscribers.
Permission Levels
Organization Owners:
Have full access and administrative control in Notifications Admin
Can grant administrative access to groups in the Permissions section
Group Members:
Have full access rights to subscription lists
Can view the History log
Assign Notifications Permissions
Organization Owners can assign permissions to a Group. The Groups for your Organization will populate the list and permissions are applied or removed as soon as the state of the toggle is updated.
Navigate to your organization's Notifications site (http://notifications.civicplus.com/[orgname]/admin)
Click Administration and select Permissions

Find the group you want to assign permissions to and click the Has Access toggle to the right of the group name to assign permissions

Note: The toggle is "on" when it is on the right.