Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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×#4716 | C2 | semidirect |
| 4. C3×#4466 | C2 | semidirect |
| 5. #10589136 | C2 | semidirect |
| 6. #10589130 | C2 | semidirect |
| 21. #63551 | C4 | semidirect |
| 22. #63549 | C4 | semidirect |
| 29. #4716 | D3 | semidirect |
| 37. #4466 | D3 | semidirect |
| 257. C32 | #2180 | semidirect |
| 290. C3 | #69090 | semidirect |
| 291. C3 | #70917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592416 | 2 |
| C3×#4716 | 2 |
| #10590642 | 2 |
| C3×#4466 | 2 |
| #10589136 | 2 |
| #10589130 | 2 |
| #10589125 | 2 |
| #70917 | 3 |
| #69090 | 3 |