The oxides A(3)M'MO6 (M = Rh, Ir: A = Ca, Sr; M' = alkaline earth, Zn, Cd) of the K4CdCl6 structure type consist of isolated (MO6)(8-) octahedral anions and exhibit an antiferromagnetic ordering at low temperatures. The spin-spin interactions in these oxides, Ca3NaMO6 (M = Ir, Ru), and Sr3NaRuO6 were examined by calculating how strongly the t(2g)-block levels of adjacent (MO6)((6+n)-) (n = 1, 2) anions interact in the presence and absence of the intervening cations A(2+) and M' (n+) (n = I, 2). Our calculations show that the spin-spin interactions in these oxides are three-dimensional, and the superexchange interactions occur mainly through the short intrachain and interchain M-O ... O-M linkages. When the Mn+ cation is very small compared with the A(2+) cation, the intrachain interaction is substantially stronger than the interchain interaction. The opposite is found when the sizes of the Mn+ and A(2+) cations become similar.