Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20251764 | C2 | semidirect |
| 4. #20241247 | C2 | semidirect |
| 5. #20241246 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 44. C4⋊Q8×C47 | Q8 | semidirect |
| 45. #127×C47 | Q8 | semidirect |
| 193. C47 | #10362 | semidirect |
| 199. C4⋊Q8 | Dic94 | semidirect |
| 200. #127 | Dic94 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251764 | 2 |
| #20244217 | 2 |
| #20241948 | 2 |
| #20241247 | 2 |
| #20241246 | 2 |
| #20241220 | 2 |
| C47×#1517 | 2 |
| #10362 | 47 |