Creating Alert is easy enough, but there are tricks to add AD groups.
The first trick is that the groups need to be ‘email enabled security groups’. Distribution lists do not show up in the people picker.
The second trick, and the one that is not documented is that you will need to explicitly add the group that you intend to email to a permission group in the site collection, site, or list, etc…
To do that, I always created a SharePoint group, then give the right permission to the group for the site. Then add AD groups to the SharePoint group.