Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
489 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10592379 | C2 | semidirect |
| 3. #10590369 | C2 | semidirect |
| 4. #10590273 | C2 | semidirect |
| 5. C3×#4455 | C2 | semidirect |
| 27. #4455 | D3 | semidirect |
| 72. C32×C8 | SD16 | semidirect |
| 151. C3×C8 | #204 | semidirect |
| 152. C3×C8 | #214 | semidirect |
| 190. C32 | #1715 | semidirect |
| 202. C8 | #3716 | semidirect |
| 222. C3 | #68091 | semidirect |
| 223. C3 | #71277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592379 | 2 |
| C3×#4695 | 2 |
| #10590369 | 2 |
| #10590273 | 2 |
| C3×#4455 | 2 |
| #71277 | 3 |
| #68091 | 3 |