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Abstract The field of Mie‐resonant nanophotonics has attracted a lot of attention recently due to many promising applications in linear and nonlinear metaoptics. Optically induced magnetic resonances define novel characteristics of isolated high‐index dielectric nanoparticles and their oligomers. Here, the orientation‐dependent nonlinear frequency generation from dielectric oligomers with different symmetries, being all characterized by isotropic linear response, is demonstrated. The rotational dependence of the third‐harmonic signal emitted by the nanoparticle oligomers in accord with their point‐group symmetry (e.g., C3 or C4) is observed experimentally, while their linear scattering remains isotropic. The experimental data are in a good agreement with numerical simulations and the symmetry analysis of the nonlinear susceptibility tensor. The results open a new avenue for tailoring nonlinear properties of nanoscale structures.