Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 1. C9×#895 | C2 | semidirect |
| 2. #11721038 | C2 | semidirect |
| 3. C2×#88422 | C2 | semidirect |
| 4. C2×#88420 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. C3×#63367 | C2 | semidirect |
| 7. #11720294 | C2 | semidirect |
| 37. #63367 | D3 | semidirect |
| 54. C3×C9⋊C8 | D4 | semidirect |
| 108. #895 | D9 | semidirect |
| 155. C9⋊C8 | D12 | semidirect |
| 236. C3×C9 | #469 | semidirect |
| 345. C9 | #4865 | semidirect |
| 395. C3 | #10588722 | 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×#88420 | 2 |
| #11720528 | 2 |
| C3×#63367 | 2 |
| #11720294 | 2 |
| #10590586 | 3 |
| #10588722 | 3 |