Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1042 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1042 conjugacy classes of subgroups — too many to draw. Only its 207 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. C22×C9×D12 | C2 | semidirect |
| 2. C2×C9×(C2×D3)⋊C4 | C2 | semidirect |
| 3. C3×C9×#95 | C2 | semidirect |
| 18. C9×#95 | D3 | semidirect |
| 24. C22×D3×C9 | D4 | semidirect |
| 26. C2×C3×C4×C9 | D4 | semidirect |
| 30. #4671 | C9 | direct (N × H) |
| 55. C22×D12 | C2×C9 | semidirect |
| 57. C2×(C2×D3)⋊C4 | C2×C9 | semidirect |
| 59. C3×#95 | C2×C9 | semidirect |
| 83. C2×C4×C9 | D12 | semidirect |
| 128. #95 | D3×C9 | semidirect |
| 129. C3×C9 | #392 | semidirect |
| 142. C22×D3 | D4×C9 | semidirect |
| 149. C2×C3×C4 | D4×C9 | semidirect |
| 196. C9 | #4671 | direct (N × H) |
| 206. C2×C4 | C9×D12 | semidirect |
| 229. C3 | C9×#392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×D12 | 2 |
| C2×C9×(C2×D3)⋊C4 | 2 |
| C3×C9×#95 | 2 |
| C3×#4671 | 3 |
| C9×#392 | 3 |