Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 105 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×#893 | C2 | semidirect |
| 2. #11720993 | C2 | semidirect |
| 4. #11720528 | C2 | semidirect |
| 5. C3×#63366 | C2 | semidirect |
| 6. #11720294 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 21. #88422 | C4 | semidirect |
| 35. #63366 | D3 | semidirect |
| 42. C4⋊(C3⋊D9) | C2×C4 | semidirect |
| 47. C9×D12 | C2×C4 | semidirect |
| 51. C3×C9⋊C8 | C2×C4 | semidirect |
| 92. C9×Dic3 | D8 | semidirect |
| 98. #893 | D9 | semidirect |
| 144. C9⋊C8 | C4×D3 | semidirect |
| 218. C3×C9 | C4×D8 | semidirect |
| 246. D12 | C4×D9 | semidirect |
| 313. Dic3 | #3673 | semidirect |
| 316. C9 | #4872 | semidirect |
| 360. C3 | C4×#3673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#893 | 2 |
| #11720993 | 2 |
| C2×#88422 | 2 |
| #11720528 | 2 |
| C3×#63366 | 2 |
| #11720294 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590456 | 3 |
| C4×#3673 | 3 |