Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
311 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10590810 | C2 | semidirect |
| 4. #10589383 | C2 | semidirect |
| 6. C3×#4512 | C2 | semidirect |
| 7. #10589136 | C2 | semidirect |
| 21. #63551 | C4 | semidirect |
| 22. #63548 | C4 | semidirect |
| 36. #4512 | D3 | semidirect |
| 246. C32 | #2180 | semidirect |
| 278. C3 | #69090 | semidirect |
| 279. C3 | #69248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590916 | 2 |
| #10590810 | 2 |
| #10590638 | 2 |
| #10589383 | 2 |
| C3×#4518 | 2 |
| C3×#4512 | 2 |
| #10589136 | 2 |
| #69248 | 3 |
| #69090 | 3 |