Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
253 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 253 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. C9×C4⋊S4 | C2 | semidirect |
| 2. C8×C9×A4 | C2 | semidirect |
| 11. C22×C8×C9 | D3 | semidirect |
| 20. #5402 | C9 | direct (N × H) |
| 36. C9×A4 | D8 | semidirect |
| 38. C4⋊S4 | C2×C9 | semidirect |
| 43. C8×A4 | C2×C9 | semidirect |
| 62. C8×C9 | S4 | semidirect |
| 87. C22×C9 | D24 | semidirect |
| 94. C22×C8 | D3×C9 | semidirect |
| 140. A4 | C9×D8 | semidirect |
| 148. C9 | #5402 | direct (N × H) |
| 159. C8 | C9×S4 | semidirect |
| 172. C22 | C9×D24 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C4⋊S4 | 2 |
| C8×C9×A4 | 2 |
| C3×#5402 | 3 |
| C9×#466 | 3 |
| C9×D24 | 4 |