Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
381 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 381 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10592381 | C2 | semidirect |
| 4. C3×#4457 | C2 | semidirect |
| 5. #10589094 | C2 | semidirect |
| 29. #4457 | D3 | semidirect |
| 83. C32×C8 | SD16 | semidirect |
| 180. C3×C8 | #204 | semidirect |
| 181. C3×C8 | #214 | semidirect |
| 228. C32 | #1693 | semidirect |
| 243. C8 | #3716 | semidirect |
| 266. C3 | #68542 | semidirect |
| 267. C3 | #70873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592381 | 2 |
| C3×#4688 | 2 |
| #10590365 | 2 |
| C3×#4457 | 2 |
| #10589094 | 2 |
| #70873 | 3 |
| #68542 | 3 |