Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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×#895 | C2 | semidirect |
| 2. #11721038 | C2 | semidirect |
| 3. C2×#88422 | C2 | semidirect |
| 4. C2×D3×C9⋊C8 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. C3×#63366 | C2 | semidirect |
| 7. #11720294 | C2 | semidirect |
| 37. #63366 | D3 | semidirect |
| 54. C3×C9⋊C8 | D4 | semidirect |
| 95. C2×D3×C9 | D8 | semidirect |
| 108. #895 | D9 | semidirect |
| 155. C9⋊C8 | D12 | semidirect |
| 236. C3×C9 | #466 | semidirect |
| 329. C2×D3 | #3673 | semidirect |
| 345. C9 | #4883 | semidirect |
| 395. C3 | #10588721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#895 | 2 |
| #11721038 | 2 |
| C2×#88422 | 2 |
| C2×D3×C9⋊C8 | 2 |
| #11720528 | 2 |
| C3×#63366 | 2 |
| #11720294 | 2 |
| #10590576 | 3 |
| #10588721 | 3 |