Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
200 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C2×C9×Dic6 | C2 | semidirect |
| 3. C3×C9×M16 | C2 | semidirect |
| 4. C9×Dic12 | C2 | semidirect |
| 5. C9×#204 | C2 | semidirect |
| 27. C9×M16 | D3 | semidirect |
| 35. #909 | C9 | direct (N × H) |
| 62. C2×Dic6 | C2×C9 | semidirect |
| 66. C3×M16 | C2×C9 | semidirect |
| 68. Dic12 | C2×C9 | semidirect |
| 69. #204 | C2×C9 | semidirect |
| 86. C3×C9 | #137 | semidirect |
| 119. M16 | D3×C9 | semidirect |
| 137. C9 | #909 | direct (N × H) |
| 162. C3 | C9×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#235 | 2 |
| C2×C9×Dic6 | 2 |
| C3×C9×M16 | 2 |
| C9×Dic12 | 2 |
| C9×#204 | 2 |
| C3×#909 | 3 |
| C9×#137 | 3 |