Slansky, Goldman, and Shaw have proposed a model to account for the observation of fractionally charged states. We show that in this model, there are expected to be several low-mass solitons (four being in the mass range ∼20-60 MeV) associated with the third homotopy group π3(SU(3)/SO(3))=Z4, besides a low-mass (∼30 MeV) Z2 monopole. Confirmation of these levels and hence of the model has important implications for Cabrera's results on the magnetic monopole. An efficient algorithm for the calculation of π3(G/H) for a general Lie group G and a subgroup H is developed. It is pointed out that solitons associated with the third homotopy group are predicted by some grand-unified-theory scenarios.