The Einstein crystal method was used to determine free energy differences between some crystalline structures of hard, homonuclear tetramers. The tetramers, each built of four identical hard spheres centered on vertices of a regular tetrahedron of sides equal to the sphere diameter, were arranged in such a way that the spheres formed the fcc lattice at close packing. Various sample sizes were studied and the results were extrapolated to the thermodynamic limit. It was found that the simplest structure of the tetramers, a simple cubic lattice of molecular mass centres with all the molecules having the same orientation, shows the highest free energy amongst the studied ones. The most stable structure of the studied ones was also found.