Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
812 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 158 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. #11723354 | C2 | semidirect |
| 3. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C32×#819 | C2 | semidirect |
| 5. #11722045 | C2 | semidirect |
| 12. C3×#3746 | C4 | semidirect |
| 13. C3×#3745 | C4 | semidirect |
| 14. C3×#3744 | C4 | semidirect |
| 27. C3×#819 | D3 | semidirect |
| 54. #3746 | Dic3 | semidirect |
| 55. #3745 | Dic3 | semidirect |
| 56. #3744 | Dic3 | semidirect |
| 78. #819 | C3⋊D3 | semidirect |
| 158. C33 | #443 | semidirect |
| 222. C32 | #4895 | semidirect |
| 223. C32 | #5196 | semidirect |
| 250. C3 | #10590919 | semidirect |
| 251. C3 | #10592594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64113 | 2 |
| #11723354 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| C32×#819 | 2 |
| #11722045 | 2 |
| #10592594 | 3 |
| #10590919 | 3 |