Enhance UI to control which Groups show in Alert widget

We have devices that need to be members of multiple groups to keep our notifications simple.  Currently, in the alert widget, all group memberships are shown in the Group column.  We would like to be able to select which groups should be visible in the Group column.  Usually it's the main business service group, and not the technical groups used only for alert rules.

Also, we would like the groups in the Group column to be alphabetically sorted.  Order seems random at the moment.  Readability would be improved also if each group in the Group column was on a new line.