That accounts for all but 210 of the octads. S permutes the 3 octads bodily. A trio is a set of 3 disjoint octads of the Golay code. PSL(2,7) permutes the octads internally, in parallel. An S(5,8,24) system would have 759 blocks, or octads. Those remaining octads are subsets of W and are symmetric differences of pairs of lines.