Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 341 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 |
|---|---|---|
| 1. #10592594 | C2 | semidirect |
| 2. #10590919 | C2 | semidirect |
| 4. C3×#4497 | C2 | semidirect |
| 5. C3×#4493 | C2 | semidirect |
| 6. #10589122 | C2 | semidirect |
| 7. #10589104 | C2 | semidirect |
| 21. #63551 | C4 | semidirect |
| 22. #63549 | C4 | semidirect |
| 23. #63548 | C4 | semidirect |
| 24. #63546 | C4 | semidirect |
| 38. #4497 | D3 | semidirect |
| 39. #4493 | D3 | semidirect |
| 281. C32 | #2179 | semidirect |
| 318. C3 | #69239 | semidirect |
| 319. C3 | #69358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592594 | 2 |
| #10590919 | 2 |
| #10590632 | 2 |
| C3×#4497 | 2 |
| C3×#4493 | 2 |
| #10589122 | 2 |
| #10589104 | 2 |
| #69358 | 3 |
| #69239 | 3 |