sql server 2008 email notifications
Have you created a contact group in Outlook or a Distribution group in Exchange? (I'm assuming you are using Exchange?)

The Outlook group is just a container that lets you send emails to many people from your personal machine.  The SQL Server is trying to send to a group that exists only on your Outlook and not on the Exchange server which is why single email recipients work but not the group.

I would suggest setting up, or asking your email admin to setup a new SQL support distribution group on your mail server.

or

You can send to multiple single email addresses by separating the address of the recipient with a ;