The microwave power dependence of the collective translational domain wall resonance spectra in garnet films with a perpendicular anisotropy supporting parallel stripe domains has been investigated using broadband ferromagnetic resonance experiments. Besides the fundamental domain wall resonances, a narrow subharmonic resonance at half the frequency of the fundamental Bloch domain wall resonance is revealed. For each domain wall resonance, the power dependences of the resonance frequency, the resonance linewidth and the amplitude of the power absorption at resonance have been studied. The narrow subharmonic domain wall resonance appears from a moderate input microwave power far below the values for the saturation of the fundamental domain wall resonances and its amplitude at resonance follows a nearly quadratic dependence on the microwave power. An analytical model based on the nonlinear Slonczewski's equation for the domain wall dynamics serves as a guide to justify the existence of such a subharmonic domain wall resonance and highlights the effect of an oblique pumping field configuration in accordance to our experimental setup.