Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×#4682 | C2 | semidirect |
| 4. C3×#4457 | C2 | semidirect |
| 5. #10589093 | C2 | semidirect |
| 25. #4682 | D3 | semidirect |
| 29. #4457 | D3 | semidirect |
| 84. C32×C8 | SD16 | semidirect |
| 185. C3×C8 | #204 | semidirect |
| 186. C3×C8 | #215 | semidirect |
| 238. C32 | #1693 | semidirect |
| 253. C8 | #3717 | semidirect |
| 277. C3 | #68542 | semidirect |
| 278. C3 | #71373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592387 | 2 |
| C3×#4682 | 2 |
| #10590379 | 2 |
| C3×#4457 | 2 |
| #10589093 | 2 |
| #71373 | 3 |
| #68542 | 3 |