Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
310 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 37. #13093960 | Q8 | semidirect |
| 52. M32×C47 | Q8 | semidirect |
| 54. C2×C16×C47 | Q8 | semidirect |
| 150. C47 | #13460 | semidirect |
| 166. M32 | Dic94 | semidirect |
| 168. C2×C16 | Dic94 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253919 | 2 |
| #20245161 | 2 |
| C2×#15688946 | 2 |
| #20244178 | 2 |
| #20241503 | 2 |
| #20241487 | 2 |
| C47×#1378 | 2 |
| #13460 | 47 |