While the (classical) ground state structure of an atomic monolayer adsorbed at a smooth substrate with negligible corrugation potential is trivial, namely, a triangular lattice with a spacing given by the minimum of the interatomic (Lennard-Jones) potential, nontrivial ground state structures occur on corrugated substrate surfaces. Assuming as a substrate surface the (100) plane of a face-centered cubic crystal, the possible (classical) ground state structures of the monolayer are studied by Monte Carlo simulation, varying both the density of the adsorbed film and the strength of the potential due to the surface. Different incommensurate structures are found, which can be interpreted as (two-dimensional) patterns of domain walls separating commensurate regions. Typically the heavy walls are oriented along the face diagonals of the square substrate lattice. This nonuniform order also is reflected in the distribution of distances of the adsorbed atoms from the substrate surface plane, which is not a delta function but may even display a bimodal character.