Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
812 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 162 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. C3×#64110 | C2 | semidirect |
| 2. C32×#901 | C2 | semidirect |
| 4. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 5. #11722059 | C2 | semidirect |
| 6. #11722045 | C2 | semidirect |
| 7. #11722043 | C2 | semidirect |
| 21. #88798 | C4 | semidirect |
| 22. #88793 | C4 | semidirect |
| 23. #88792 | C4 | semidirect |
| 24. #88789 | C4 | semidirect |
| 27. #64110 | D3 | semidirect |
| 29. C3×#901 | D3 | semidirect |
| 104. #901 | C3⋊D3 | semidirect |
| 217. C33 | #443 | semidirect |
| 302. C32 | #5144 | semidirect |
| 303. C32 | #5144 | semidirect |
| 339. C3 | #10590921 | semidirect |
| 340. C3 | #10592843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64110 | 2 |
| C32×#901 | 2 |
| #11723363 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #11722059 | 2 |
| #11722045 | 2 |
| #11722043 | 2 |
| #10592843 | 3 |
| #10590921 | 3 |