The organic metal θ-(BETS)4HgBr4(C6H5Cl) is known to undergo a phase transition as the temperature is lowered down to about 240K. X-ray data obtained at 200K indicate a corresponding modification of the crystal structure, the symmetry of which is lowered from quadratic to monoclinic. In addition, two different types of cation layers are observed in the unit cell. The Fermi surface (FS), which can be regarded as a network of compensated electron and hole orbits according to band structure calculations at room temperature, turns to a set of two alternating linear chains of orbits at low temperature. The field and temperature dependence of the Shubnikov-de Haas oscillation spectrum have been studied up to 54T. Eight frequencies are observed which, in any case, point to an FS much more complex than predicted by band structure calculations at room temperature, even though some of the observed Fourier components might be ascribed to magnetic breakdown or frequency mixing. The obtained spectrum could result from either an interaction between the FSs linked to each of the two cation layers or to an eventual additional phase transition in the temperature range below 200K.