Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
362 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 362 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×#907 | C2 | semidirect |
| 3. #11720862 | C2 | semidirect |
| 4. #11720558 | C2 | semidirect |
| 5. C3×#63381 | C2 | semidirect |
| 6. #11720300 | C2 | semidirect |
| 7. #11720271 | C2 | semidirect |
| 19. #88428 | C4 | semidirect |
| 20. #88426 | C4 | semidirect |
| 21. #88424 | C4 | semidirect |
| 22. #88422 | C4 | semidirect |
| 38. #63381 | D3 | semidirect |
| 102. #907 | D9 | semidirect |
| 220. C3×C9 | #443 | semidirect |
| 310. C9 | #4895 | semidirect |
| 347. C3 | #10588824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#907 | 2 |
| #11720889 | 2 |
| #11720862 | 2 |
| #11720558 | 2 |
| C3×#63381 | 2 |
| #11720300 | 2 |
| #11720271 | 2 |
| #10590995 | 3 |
| #10588824 | 3 |