Co0 has 4 conjugacy classes of elements of order 3. In M24 an element of shape 38 generates a group normal in a copy of S3, which commutes with a simple subgroup of order 168. A direct product in M24 permutes the octads of a trio and permutes 14 dodecad diagonal matrices in the monomial subgroup. In Co0 this monomial normalizer is expanded to a maximal subgroup of the form , where 2.A9 is the double cover of the alternating group A9.