Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
654 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20252298 | C2 | semidirect |
| 2. #20252031 | C2 | semidirect |
| 3. #20244968 | C2 | semidirect |
| 4. #20244942 | C2 | semidirect |
| 6. #20244094 | C2 | semidirect |
| 7. #20243886 | C2 | semidirect |
| 8. #20243748 | C2 | semidirect |
| 9. #20243676 | C2 | semidirect |
| 10. #20243535 | C2 | semidirect |
| 11. C47×#2053 | C2 | semidirect |
| 190. #2053 | D47 | semidirect |
| 229. C47 | #29386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252298 | 2 |
| #20252031 | 2 |
| #20244968 | 2 |
| #20244942 | 2 |
| #20244491 | 2 |
| #20244094 | 2 |
| #20243886 | 2 |
| #20243748 | 2 |
| #20243676 | 2 |
| #20243535 | 2 |
| C47×#2053 | 2 |
| #29386 | 47 |