We study the stellar mass functions of early and late-type galaxies in a galaxy group system at a redshift of z=0.37 in order to investigate mass assembly histories in a type of rarely explored galaxy systems at intermediate redshifts which are progenitors of local, massive clusters. Our system, the supergroup SG1120-1202, is comprised of four galaxy groups that will merge together and form a single galaxy cluster by z=0. Galaxies are classified into early and late-types by using automated and visual methods. The early and late-type mass functions can each be fit with single Schechter functions, but the Schechter parameters differ for the two populations. The value of M* is significantly larger for early-type galaxies and their faint end slope decreases faster compared to late types. This may indicate differences in the mass assembly histories of different morphological galaxy populations in groups at intermediate redshifts.