Agree with Penny here - I've never found an "easy" way to do it, I've done with a combination of the "All Email Batch" or "Activity" report, and then done some filtering by conditions that would create the contact group. Here's the steps I follow to pull reporting after the fact to show differentiation of activity for the group vs. the filter. If more than one filter is included this gets complicated and unwieldy.
1. Export “Email Overview From Batch Sends” Report selecting the appropriate timeframe and email data.
2. Using the topline data from the “Email Overview From Batch Sends” Report (aggregated numbers from all batches) create an excel spreadsheet with stats.
3. Navigate to Communicate > Email > Lists and review the inclusion list from the original distribution lists; in your excel sheet make note of the exact names of contact filters and contact groups included in the distribution list.
4.Using the “Distribution List Part Overview by Email” Report select the distribution list, email, timeframe and contact group (list found in “Distribution List Part Value” drop-down menu) you need numbers for. If you have only contact groups included in your distribution list this report will provide you with all the numbers you need to measure each contact groups’ performance against the whole distribution list.
5. If your distribution list included contact filters you are going to need to recreate those filters and then search for the specific activity points for the particular email/date of send. This is a bit more complex as it will not generate counts of unique activities but aggregated totals.
From that I then use excel to subtract the data for the specific segments out of the overall numbers that are in the aggregate reports.