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Strong Mie-type magnetic dipole resonances in all-dielectric nanostructures provide novel opportunities for enhancing nonlinear effects at the nanoscale due to the intense electric and magnetic fields trapped within the individual nanoparticles. Here we study third-harmonic generation from quadrumers of silicon nanodisks supporting high-quality collective modes associated with the magnetic Fano resonance. We observe nontrivial wavelength and angular dependencies of the generated harmonic signal featuring a multifold enhancement of the nonlinear response in oligomeric systems.