the notification feature which you find in your supscription is optional. You have various norifications with little squares in front of them:
Email when there are messages needing approval.
Email when there are members needing approval.
Email when a member joins/leaves this group.
Email when group storage limits are reached.
Email when someone creates or deletes a subgroup.
Email when someone reports a message.
Email when someone uploads a photo
Email when someone uploads a file/database
So if you don´t check them no notification goes out.