In this article, the most relevant isomers of uranium tricarbide are studied through quantum chemical methods. It is found that the most stable isomer has a fan geometry in which the uranium atom is bonded to a quasilinear C3 unit. Both, a rhombic and a ring CU(C2) structures are found about 104-125 kJ/mol higher in energy. Other possible isomers including linear geometries are located even higher. For each structure, we provide predictions for those molecular properties (vibrational frequencies, IR intensities, dipole moments) that could eventually help in their experimental detection. We also discuss the possible routes for the formation of the different UC3 isomers as well as the bonding situation by means of a topological analysis of the electron density.