Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20244634 | C2 | semidirect |
| 2. #20244529 | C2 | semidirect |
| 4. #20241214 | C2 | semidirect |
| 5. #20241211 | C2 | semidirect |
| 223. C47 | #7773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244634 | 2 |
| #20244529 | 2 |
| #20244524 | 2 |
| #20241214 | 2 |
| #20241211 | 2 |
| #20241209 | 2 |
| C47×#2808 | 2 |
| #7773 | 47 |