Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
415 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 415 conjugacy classes of subgroups — too many to draw. Only its 108 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. #64110⋊C3 | C2 | semidirect |
| 3. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #63646⋊C3 | C2 | semidirect |
| 5. #63632⋊C3 | C2 | semidirect |
| 6. #10592399 | C3 | semidirect |
| 13. #3745⋊C3 | C4 | semidirect |
| 14. #3744⋊C3 | C4 | semidirect |
| 17. #3746⋊C3 | C4 | semidirect |
| 19. #64110 | C2×C3 | semidirect |
| 23. C32×C4×C8 | D3 | semidirect |
| 24. C32×C4×C8 | C2×C3 | semidirect |
| 25. #63646 | C2×C3 | semidirect |
| 26. #63632 | C2×C3 | semidirect |
| 55. #3746 | C3×C4 | semidirect |
| 56. #3745 | C3×C4 | semidirect |
| 57. #3744 | C3×C4 | semidirect |
| 173. C4×C8 | (C3⋊D3)⋊C3 | semidirect |
| 174. H(3,𝔽3) | #443 | semidirect |
| 255. C32 | #4700 | semidirect |
| 256. C32 | C3×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64113⋊C3 | 2 |
| #64110⋊C3 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #63646⋊C3 | 2 |
| #63632⋊C3 | 2 |
| #10592399 | 3 |
| C3×#4700 | 3 |