Police say the men broke into the woman's house in Hobart Wednesday and beat her.
As the suspects drove away, the victim's neighbor, a Hammond firefighter, chased them.
Their vehicles collided and shots were fired.
The fourth suspect shot and killed himself near the scene of the crash.
The suspects charged with felonies Friday are Dominick Fazzini, Michael Sprague and Jordan Wilkerson.
They are all being held without bond.
