By default, each contact will be the 'Bill To' contact when you are viewing your unbilled items. If you need to bill for multiple clients under one Client Group you can change each client's 'bill to' contact to the associated Client Group.
Once this has been updated, you will then be able to go back to the Unbilled section in Billing and you'll now see all of the allocated time entries under one Client Group. Select the items you'd like on the invoice and create your draft invoice.
If you need a single work items to be billed under the Client Group, you are able to change the 'Bill To' contact within the work item. This change is made in the Basics section on the Details tab of the individual work item.