We present an experimental study and develop a group theoretical analysis of the Zeeman effect on excitons in pyramidal semiconductor quantum dots possessing the symmetries of the C3v point group. The magnetic field dependence of the emission pattern originating from neutral exciton states is investigated in both the Faraday and Voigt configurations. The Zeeman doublet splitting of the “bright” exciton states varies linearly with the magnetic field strength in each configuration while the intensity of the “dark” exciton transitions exhibit a nonlinear dependence. We demonstrate that these observations originate from the intertwining of the Zeeman and Coulomb interactions, which provides clear spectral signatures of this effect for highly symmetric quantum dots. We uncover a large anisotropy of the Zeeman doublet splittings for longitudinal and transverse magnetic fields, revealing the ubiquitous role of a symmetry elevation in our pyramidal quantum dots. These results suggest that the common description of the Zeeman effect based on effective g factors for electrons and holes must be revised when dealing with exciton complexes.