Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
134 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 24. #824 | C9 | direct (N × H) |
| 60. C3×C9 | #101 | semidirect |
| 97. C9 | #824 | direct (N × H) |
| 115. C3 | C9×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Dic6 | 2 |
| C3×C9×M16 | 2 |
| C9×#208 | 2 |
| C3×#824 | 3 |
| C9×#101 | 3 |