Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
744 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 744 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×#815 | C2 | semidirect |
| 5. #11722046 | C2 | semidirect |
| 11. C3×#3746 | C4 | semidirect |
| 12. C3×#3745 | C4 | semidirect |
| 13. C3×#3744 | C4 | semidirect |
| 27. C3×#815 | D3 | semidirect |
| 51. #3746 | Dic3 | semidirect |
| 52. #3745 | Dic3 | semidirect |
| 53. #3744 | Dic3 | semidirect |
| 78. #815 | C3⋊D3 | semidirect |
| 150. C33 | #444 | semidirect |
| 209. C32 | #4717 | semidirect |
| 210. C32 | #5197 | semidirect |
| 236. C3 | #10590916 | semidirect |
| 237. C3 | #10592416 | 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×#815 | 2 |
| #11722046 | 2 |
| #10592416 | 3 |
| #10590916 | 3 |