Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
730 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 135 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. #11722673 | C2 | semidirect |
| 2. #11721867 | C2 | semidirect |
| 3. #11721783 | C2 | semidirect |
| 4. #11721712 | C2 | semidirect |
| 5. C3×C9×#104 | C2 | semidirect |
| 6. #11720556 | C2 | semidirect |
| 7. #11720518 | C2 | semidirect |
| 38. C9×#104 | D3 | semidirect |
| 118. C3×#104 | D9 | semidirect |
| 235. #104 | C3⋊D9 | semidirect |
| 237. C3×C9 | #454 | semidirect |
| 332. C9 | #4827 | semidirect |
| 376. C3 | #10588507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722673 | 2 |
| #11721867 | 2 |
| #11721783 | 2 |
| #11721712 | 2 |
| C3×C9×#104 | 2 |
| #11720556 | 2 |
| #11720518 | 2 |
| #10592526 | 3 |
| #10588507 | 3 |