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Possible planar faults (obtained by shear operations) in an ordered ternary A₂BC (Cmcm) alloy with an orthorhombic structure have been studied using a hard-sphere model. Planar faults on various planes equivalent to D0₁₉ basal, prismatic and pyramidal (first- and second-order) planes are considered and the energies of 29 antiphase boundaries, two superlattice intrinsic stacking faults and two complex stacking faults have been formulated in terms of pairwise interactions up to the seventh-nearest neighbour. These results are compared with the h.c.p.-based D0₁₉ ordered structure. The crystallography of various faults are examined on the basis of symmetry criteria using Neumann's principle. Possible dislocation dissociations on various slip planes are proposed.