Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
422 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20254291 | C2 | semidirect |
| 2. #20245300 | C2 | semidirect |
| 3. #20244495 | C2 | semidirect |
| 4. #20241406 | C2 | semidirect |
| 5. #20241404 | C2 | semidirect |
| 6. #20241313 | C2 | semidirect |
| 7. C47×#2187 | C2 | semidirect |
| 179. #2187 | D47 | semidirect |
| 211. C47 | #12110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254291 | 2 |
| #20245300 | 2 |
| #20244495 | 2 |
| #20241406 | 2 |
| #20241404 | 2 |
| #20241313 | 2 |
| C47×#2187 | 2 |
| #12110 | 47 |