Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
756 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 2. #11723352 | C2 | semidirect |
| 3. #11722189 | C2 | semidirect |
| 4. C32×C8×Dic3 | C2 | semidirect |
| 5. #11722046 | C2 | semidirect |
| 11. C3×#3746 | C4 | semidirect |
| 12. C3×#3745 | C4 | semidirect |
| 13. C3×#3744 | C4 | semidirect |
| 27. C3×C8×Dic3 | D3 | semidirect |
| 52. #3746 | Dic3 | semidirect |
| 53. #3745 | Dic3 | semidirect |
| 54. #3744 | Dic3 | semidirect |
| 79. C8×Dic3 | C3⋊D3 | semidirect |
| 153. C33 | #443 | semidirect |
| 214. C32 | #4700 | semidirect |
| 215. C32 | #5196 | semidirect |
| 242. C3 | #10590915 | semidirect |
| 243. C3 | #10592399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64113 | 2 |
| #11723352 | 2 |
| #11722189 | 2 |
| C32×C8×Dic3 | 2 |
| #11722046 | 2 |
| #10592399 | 3 |
| #10590915 | 3 |