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It is known that the nonlinear optical properties of photonic nanostructures can be modified substantially due to strong field confinement and optical resonances. In this contribution, we study third-harmonic generation from low-loss subwavelength silicon nanodisks arranged in the form of trimer oligomers with varying distance between the nanoparticles. Each of the nanodisks exhibits both electric and magnetic Mie-type resonances that are shown to affect significantly the nonlinear response. We observe the third-harmonic radiation intensity that is comparable to that of a bulk silicon slab and demonstrate a pronounced reshaping of the third-harmonic spectra due to interference of the nonlinearly generated waves augmented by an interplay between the electric and the magnetic dipolar resonances.