Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1067 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1067 conjugacy classes of subgroups — too many to draw. Only its 209 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. #11721689 | C2 | semidirect |
| 3. C2×#88435 | C2 | semidirect |
| 4. #11721065 | C2 | semidirect |
| 5. #11721064 | C2 | semidirect |
| 14. #3748⋊C3 | C22 | semidirect |
| 15. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 18. #88435 | C22 | semidirect |
| 19. #88434 | C22 | semidirect |
| 22. #64157 | D3 | semidirect |
| 58. #3748 | C2×D3 | semidirect |
| 59. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 178. H(3,𝔽3) | #568 | semidirect |
| 267. C32 | #5750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#272 | 2 |
| #11721689 | 2 |
| C2×#88435 | 2 |
| #11721065 | 2 |
| #11721064 | 2 |
| #10595441 | 3 |