Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
415 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 415 conjugacy classes of subgroups — too many to draw. Only its 114 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. C32×#446 | C2 | semidirect |
| 2. C3×#5027 | C2 | semidirect |
| 4. C3×#4485 | C2 | semidirect |
| 5. C3×#4457 | C2 | semidirect |
| 7. #70959 | C3 | direct (N × H) |
| 22. C3×#446 | D3 | semidirect |
| 23. C3×#446 | C2×C3 | semidirect |
| 24. #5027 | C2×C3 | semidirect |
| 28. #4485 | C2×C3 | semidirect |
| 29. #4457 | C2×C3 | semidirect |
| 87. C32×C8 | SD16 | semidirect |
| 91. #446 | C3×D3 | semidirect |
| 191. C3×C8 | #215 | semidirect |
| 192. C3×C8 | C3×SD16 | semidirect |
| 240. C32 | #1688 | semidirect |
| 256. C8 | C3×#215 | semidirect |
| 279. C3 | #70959 | direct (N × H) |
| 280. C3 | C3×#1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#446 | 2 |
| C3×#5027 | 2 |
| C3×#4695 | 2 |
| C3×#4485 | 2 |
| C3×#4457 | 2 |
| C3×#1688 | 3 |
| #70959 | 3 |