The three isostructural magnetic oxides MAs2O6 (M = Mn, Co, Ni) containing high-spin M(2+) ions undergo a long-range antiferromagnetic ordering below 30 K, but their ordered magnetic structures are not identical. While CoAs2O6 and NiAs2O6 adopt the commensurate superstructure of q1 = (0, 0, 1/2), MnAs2O6 has the incommensurate superstructure of q2 = (0.055, 0.389, 0.136). The cause for this difference was examined by calculating their spin exchange and magnetic dipole-dipole interaction energies. In CoAs2O6 and NiAs2O6, the strongest M-O···O-M spin exchange, J1, dominates over other exchanges, hence leading to the q1 superstructure. For MnAs2O6, the spin exchanges are not a deciding factor leading to its magnetic superstructure, being all weak and comparable in strengths, but the magnetic dipole-dipole interactions are.