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We report the experimental results of third harmonic generation (THG) spectroscopy of silicon nanodisk oligomers that reveal the contributions of magnetic and electric dipolar resonances to the third-order nonlinear-optical response. Due to the local field enhancement of the pump beam upon excitation of the oligomer resonances, the THG is strongly enhanced with respect to the bulk crystalline silicon. By changing the oligomer geometry we bring both resonances to a partial overlap, which causes a strong THG enhancement for wavelengths of the strongest overlap. This effect is explained in the framework of constructive interference of the third harmonic signal generated by the electric and magnetic dipolar resonances.