Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1016 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 1016 conjugacy classes of subgroups — too many to draw. Only its 154 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×#88862 | C2 | semidirect |
| 2. C32×#947 | C2 | semidirect |
| 3. #11723484 | C2 | semidirect |
| 5. C3×#63662 | C2 | semidirect |
| 6. Dic3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 7. #11722031 | C2 | semidirect |
| 29. C3×#947 | D3 | semidirect |
| 32. #63662 | D3 | semidirect |
| 100. #947 | C3⋊D3 | semidirect |
| 230. C33 | #463 | semidirect |
| 332. C32 | #4819 | semidirect |
| 333. C32 | #5057 | semidirect |
| 378. C3 | #10591568 | semidirect |
| 379. C3 | #10592756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88862 | 2 |
| C32×#947 | 2 |
| #11723484 | 2 |
| C2×#88790 | 2 |
| C3×#63662 | 2 |
| Dic3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722031 | 2 |
| #10592756 | 3 |
| #10591568 | 3 |