We investigate experimentally and theoretically the nonlinearly diffracted second harmonic light from the first-order Hermite-Gauss beam. We investigate the cases of loosely and tightly focused beams in a periodically poled lithium niobate crystal in the temperature range near the birefringent phase matching. Unlike the case of fundamental Gaussian beam, the nonlinear diffracted beam is spatially structured. Its shape depends on the focusing conditions and on the crystal temperature. Furthermore, for the case of tight focusing, the diffracted beam structure depends on the beam's position with respect to the domain wall.