Hi Balram,
SLAs (service type events) are attached to tickets based on attributes such as priority, but I do not think you can control SLA timers directly via the group field. I thought about something like this...have multiple service type events, one with the condition being the priority of the case (which is the normal SLA functionality/usage) and another for the condition being the group on the case. However, I now realize that this wouldn't work for two reasons... one, the higher ranking SLA would take precedence (meaning the one thats less hours), and two, even if the precedence part was not an issue, it would actually swap the SLA back and forth between the two, and that would restart it rather than just stopping a clock and starting it. SO, unfortunately I dont think this would work. I would say the best bet for this one would be to post it as an idea here in the communities and see if folks vote for it.
Regards,
Jon I.