We report the observation of large electronic g-factors in magic number main group bimetallic nanoclusters by performing Stern-Gerlach deflection experiments at 10 K. The clusters AlPb12 and InPb12 exhibit values of g = 3.5-4.0, whereas GaPb12 clusters surprisingly reveal a value of g < 2.0. Multireference ab initio methods are applied to unmask the origin of the g-factors and to gain insight into the electronic structure. The interplay of the pyritohedral molecular symmetry, a particularly strong spin-orbit coupling involved in the ground state, and the presence of low-lying degenerate excited states causes large positive g-factors in AlPb12 and InPb12. Contrarily, the spin-orbit coupling in the GaPb12 ground state is completely quenched. This is due to the d-block contraction lowering the nonbonding Ga 5s orbital and consequently forming an icosahedral ground state. Thus, endohedral p-doped tetrel clusters, composed of purely main group elements, state a novel and unique class of magnetic compounds and their study contributes to a more profound understanding of the metal-metal interaction in polynuclear clusters as well as magnetism at the molecular level.