Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11721782 | C2 | semidirect |
| 3. #11720878 | C2 | semidirect |
| 4. C9×#825 | C2 | semidirect |
| 5. C3×#63381 | C2 | semidirect |
| 6. #11720261 | C2 | semidirect |
| 7. #11720258 | C2 | semidirect |
| 19. #88428 | C4 | semidirect |
| 20. #88426 | C4 | semidirect |
| 21. #88424 | C4 | semidirect |
| 22. #88422 | C4 | semidirect |
| 37. #63381 | D3 | semidirect |
| 111. #825 | D9 | semidirect |
| 224. C3×C9 | #444 | semidirect |
| 314. C9 | #4894 | semidirect |
| 351. C3 | #10588503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721782 | 2 |
| #11720889 | 2 |
| #11720878 | 2 |
| C9×#825 | 2 |
| C3×#63381 | 2 |
| #11720261 | 2 |
| #11720258 | 2 |
| #10590978 | 3 |
| #10588503 | 3 |