From: http://en.wikipedia.org/wiki/Space_Shuttle_Challenger_disast...

The more robustly constructed crew cabin also survived the breakup of the launch vehicle; while the SRBs were subsequently destroyed remotely by the Range Safety Officer, the detached cabin continued along a ballistic trajectory and was observed exiting the cloud of gases at T+75.237.

In the images, you can see the solid rocket booster (SRB) following a random path after the explosion.