Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1152 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 164 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. #11723992 | C2 | semidirect |
| 3. #11723429 | C2 | semidirect |
| 4. #11723379 | C2 | semidirect |
| 5. C3×#63664 | C2 | semidirect |
| 6. #11722044 | C2 | semidirect |
| 7. #11722025 | C2 | semidirect |
| 11. C2×#6308 | C22 | semidirect |
| 21. #88855 | C22 | semidirect |
| 22. C3×C4×C3⋊Dic3 | C22 | semidirect |
| 23. C3×#3748 | C22 | semidirect |
| 37. #63664 | D3 | semidirect |
| 95. C4×C3⋊Dic3 | C2×D3 | semidirect |
| 99. #3748 | C2×D3 | semidirect |
| 267. C33 | #455 | semidirect |
| 382. C32 | #4825 | semidirect |
| 383. C32 | #5242 | semidirect |
| 432. C3 | #10591688 | semidirect |
| 433. C3 | #10592941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1009 | 2 |
| #11723992 | 2 |
| #11723429 | 2 |
| #11723379 | 2 |
| C3×#63664 | 2 |
| #11722044 | 2 |
| #11722025 | 2 |
| #10592941 | 3 |
| #10591688 | 3 |