We study a novel six-dimensional gauge theory compactified on the T2/7L3 orbifold utilizing the diagonal embedding method. The bulk gauge group is G x G x G, and the diagonal part Gdiag remains manifest in the effective four-dimensional theory. Further spontaneous breaking of the gauge symmetry occurs through the dynamics of the zero modes of the extradimensional components of the gauge field. We apply this setup to the SU(5) grand unified theory and examine the vacuum structure determined by the dynamics of the zero modes. We find bulk matter contents that radiatively induce spontaneous breakings of the unified symmetry Gdiag approximately equal to SU(5) down to SU(3) x SU(2) x U(1) at the global minima of the one-loop effective potential for the zero modes. This spontaneous breaking provides notable features such as a realization of the doublet-triplet splitting without a fine tuning and a prediction of light adjoint fields.