Add reminder to notify a group rather than an individual

We currentlyuse the Add Reminder option in the porcess to send emails to the Asignee and originator of an Incident. We now need to be able to send mail base on the assigned group rather than assigned analyst.

I have looked how the Reminders are setup in object designed, I can't work out how this works. So how does the system get the assigned analyst to use it as a recipient. Currently reminders only work when the assigned analyst is populated so need it to send mail when only the group is assigned and to send to all Analysts in that group.

Any Ideas?

Thanks,