The importance of triplet states in the photorelaxation dynamics of SO2 is studied by mixed quantum-classical dynamics simulations. Using the SHARC method, standing for Surface Hopping including ARbitrary Couplings, intersystem crossing (ISC) processes caused by spin-orbit coupling are found occurring on an ultrafast time scale (few 100 fs) and thus competing with internal conversion. While in the singlet-only dynamics only oscillatory population transfer between the (1)B1 and (1)A2 states is observed, in the dynamics including singlet and triplet states we find additionally continuous ISC to the (3)B2 state and to a smaller extent to the (3)B1/(3)A2 coupled states. The populations obtained from the dynamics are discussed with respect to the overall nuclear motion and in the light of recent TRPEPICO studies [I. Wilkinson, A. E. Boguslavskiy, J. Mikosch, D. M. Villeneuve, H.-J. Wörner, M. Spanner, S. Patchkovskii, and A. Stolow, "Excited state dynamics in SO2. I. Bound state relaxation studied by time-resolved photoelectron-photoion coincidence spectroscopy," J. Chem. Phys. 140, 204301 (2014)].