Mode-group multiplexing (MGM) can increase the capacity of short-reach few-mode optical fiber communication links while avoiding complex digital signal processing. In this paper, we present the design and experimental demonstration of a novel mode-group demultiplexer (MG DeMux) using Fabry-Perot (FP) thin-film filters (TFFs). The MG DeMux supports low-crosstalk mode-group demultiplexing, with degeneracies commensurate with those of graded-index (GRIN) multimode fibers. We experimentally demonstrate this functionality by using a commercial six-cavity TFF that was intended for 100 GHz channel spaced wavelength-division multiplexing (WDM) system.