Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
437 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 437 conjugacy classes of subgroups — too many to draw. Only its 98 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. #10592801 | C2 | semidirect |
| 5. C3×#4552 | C2 | semidirect |
| 6. #10589169 | C2 | semidirect |
| 7. #10589158 | C2 | semidirect |
| 35. #4552 | D3 | semidirect |
| 339. C32 | #2080 | semidirect |
| 391. C3 | #68935 | semidirect |
| 392. C3 | #70294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592801 | 2 |
| C3×#5113 | 2 |
| #10591110 | 2 |
| #10591076 | 2 |
| C3×#4552 | 2 |
| #10589169 | 2 |
| #10589158 | 2 |
| #70294 | 3 |
| #68935 | 3 |