Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
724 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 126 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. C33×#99 | C2 | semidirect |
| 3. C32×#834 | C2 | semidirect |
| 5. C3×#4474 | C3 | direct (N × H) |
| 9. C2×C32×D12 | C4 | semidirect |
| 12. C32×C4×Dic3 | C4 | semidirect |
| 17. C32×#99 | D3 | semidirect |
| 18. C32×#99 | C2×C3 | semidirect |
| 19. C3×#834 | C2×C3 | semidirect |
| 32. #4474 | C32 | direct (N × H) |
| 41. C2×C3×D12 | C3×C4 | semidirect |
| 48. C3×C4×Dic3 | C3×C4 | semidirect |
| 65. C3×#99 | C3×D3 | semidirect |
| 66. C3×#99 | C2×C32 | semidirect |
| 67. #834 | C2×C32 | semidirect |
| 109. C2×D12 | C32×C4 | semidirect |
| 116. C4×Dic3 | C32×C4 | semidirect |
| 150. #99 | C32×D3 | semidirect |
| 151. C33 | #353 | semidirect |
| 232. C32 | #4474 | direct (N × H) |
| 233. C32 | C3×#353 | semidirect |
| 272. C3 | C3×#4474 | direct (N × H) |
| 273. C3 | C32×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#940 | 2 |
| C33×#99 | 2 |
| C32×#834 | 2 |
| C32×#353 | 3 |
| C3×#4474 | 3 |