Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
374 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 374 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. #11721770 | C2 | semidirect |
| 2. C9×#901 | C2 | semidirect |
| 4. C3×#63375 | C2 | semidirect |
| 5. #11720301 | C2 | semidirect |
| 6. #11720292 | C2 | semidirect |
| 7. #11720285 | C2 | semidirect |
| 21. #88428 | C4 | semidirect |
| 22. #88426 | C4 | semidirect |
| 23. #88424 | C4 | semidirect |
| 24. #88422 | C4 | semidirect |
| 39. #63375 | D3 | semidirect |
| 107. #901 | D9 | semidirect |
| 224. C3×C9 | #444 | semidirect |
| 314. C9 | #4717 | semidirect |
| 351. C3 | #10588825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721770 | 2 |
| C9×#901 | 2 |
| #11720889 | 2 |
| C3×#63375 | 2 |
| #11720301 | 2 |
| #11720292 | 2 |
| #11720285 | 2 |
| #10590924 | 3 |
| #10588825 | 3 |