Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
896 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 144 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. C2×#88851 | C2 | semidirect |
| 2. C3×#64110 | C2 | semidirect |
| 3. #11723388 | C2 | semidirect |
| 5. C32×#819 | C2 | semidirect |
| 6. #11722030 | C2 | semidirect |
| 7. #11722027 | C2 | semidirect |
| 30. #64110 | D3 | semidirect |
| 37. C3×#819 | D3 | semidirect |
| 115. #819 | C3⋊D3 | semidirect |
| 226. C33 | #471 | semidirect |
| 317. C32 | #4898 | semidirect |
| 318. C32 | #5141 | semidirect |
| 355. C3 | #10590931 | semidirect |
| 356. C3 | #10592597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88851 | 2 |
| C3×#64110 | 2 |
| #11723388 | 2 |
| #11723371 | 2 |
| C32×#819 | 2 |
| #11722030 | 2 |
| #11722027 | 2 |
| #10592597 | 3 |
| #10590931 | 3 |