Here we study theoretically the optical responses of hybrid structures composed of dielectric nanostructures and quantum emitters with magnetic dipole transitions. Coherent couplings between magnetic dipole transitions and magnetic modes can occur, leading to giant modifications of the extinction spectra of the constituents in the hybrid structures. For a given hybrid structure, the extinction-cross-section spectra show linear or nonlinear behaviors depending on the strength of the excitation field. For a weak excitation, the extinction of the quantum emitters is greatly enhanced. The hybrid structure shows a dip on its extinction spectrum. For a strong excitation, the resonant extinction of the quantum emitters is weakly enhanced while the extinction spectrum is broadened obviously. The hybrid structure shows a Fano-like line shape on its extinction spectrum, which is different from that with a weak excitation. This difference is highly related to the behaviors of the magnetic polarizabilities of the quantum emitters in the hybrid structure. The optical responses of hybrid structures can be largely tuned by varying the geometric and material parameters.