We present a combined x-ray and neutron diffraction study of the stripe-ordered superconductor La₀Sr_0.12CuO₄. The average crystal structure is consistent with the orthorhombic Bmab space group as commonly reported in the literature. This structure, however, is not symmetry compatible with a second-order phase transition into the stripe order phase, and as we report here, numerous Bragg peaks forbidden in the Bmab space group are observed. We have studied and analyzed these Bmab-forbidden Bragg reflections. Fitting of the diffraction intensities yields monoclinic lattice distortions that are symmetry consistent with charge stripe order.