Magnetic susceptibility and specific heat measurements have been performed on two-dimensional spin systems ( M²⁺ Cl)LaNb₂O₇ ( M = Mn ( S = 5/2), Cr ( S = 2), Co ( S = 3/2)), prepared via a topotactic ion-exchange reaction. All three compounds establish antiferromagnetic order at T_N = 53 K, 61 K and 52 K, respectively for M = Mn, Co, Cr. Together with T_N = 78 K for M = Fe ( S = 2), this result indicates that the T_N is not simply scaled by the magnitude of spin. In particular, the presence of strong spin-orbit interactions is suggested for (CoCl)LaNb₂O₇ .