Alliance Air (CD) operates *old* 737-200s. It is a subsidiary of Indian Airlines (IC) and these planes were once part of the IC fleet. But now IC operates an all-Airbus fleet comprising 31 A320s and a dozen-odd older A300s, while CD runs the 732s.
In most cases CD operates between small cities and the first and last flights between metros (Delhi, Bombay, Calcutta, Madras and Bangalore) when demand is low. The hijacked flight CD7444 BOM-DEL was the last flight of the day.