Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
338 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. #10592415 | C2 | semidirect |
| 4. C3×#4466 | C2 | semidirect |
| 5. #10589137 | C2 | semidirect |
| 6. #10589131 | C2 | semidirect |
| 21. #63551 | C4 | semidirect |
| 22. #63548 | C4 | semidirect |
| 37. #4466 | D3 | semidirect |
| 255. C32 | #2180 | semidirect |
| 287. C3 | #69090 | semidirect |
| 288. C3 | #70928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592415 | 2 |
| C3×#4717 | 2 |
| #10590638 | 2 |
| C3×#4466 | 2 |
| #10589137 | 2 |
| #10589131 | 2 |
| #10589124 | 2 |
| #70928 | 3 |
| #69090 | 3 |