Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
514 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 77 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. #11722465 | C2 | semidirect |
| 2. #11721836 | C2 | semidirect |
| 3. C9×#932 | C2 | semidirect |
| 4. C3×#63495 | C2 | semidirect |
| 5. #11720300 | C2 | semidirect |
| 6. #11720291 | C2 | semidirect |
| 7. #11720290 | C2 | semidirect |
| 38. #63495 | D3 | semidirect |
| 123. #932 | D9 | semidirect |
| 262. C3×C9 | #454 | semidirect |
| 376. C9 | #5201 | semidirect |
| 424. C3 | #10588881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722465 | 2 |
| #11721836 | 2 |
| C9×#932 | 2 |
| C3×#63495 | 2 |
| #11720300 | 2 |
| #11720291 | 2 |
| #11720290 | 2 |
| #10591524 | 3 |
| #10588881 | 3 |