When doing a group booking, you will not get the cheapest fare buckets as these are restricted to a few tickets, so the per person fare will basically always be higher than the cheapest fare you can find online.

Easyjet is the only airline I know of which allows bookings for up to 40 pax on their website, for all other airlines you have to mail or call. It's a time-consuming and often frustrating task, but there's no way around it apart from using a travel agent, who will of course charge you a fee for all the work involved...

In my experience, the bigger the aircraft you're trying to book on, the bigger the chance for a decent group fare as there is more total seat availability. I did a group booking MUC-MAN recently and the cheapest fare was on Singapore Airlines' B777 (including checked baggage and full service), while Easyjet and Lufthansa quoted much higher group fares on their A319/320. Individual fares would have been quite similar.