Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
742 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 742 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. #20254145 | C2 | semidirect |
| 2. #20252650 | C2 | semidirect |
| 4. #20243299 | C2 | semidirect |
| 5. #20241751 | C2 | semidirect |
| 6. #20241264 | C2 | semidirect |
| 7. C47×#1471 | C2 | semidirect |
| 244. #1471 | D47 | semidirect |
| 279. C47 | #9975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254145 | 2 |
| #20252650 | 2 |
| #20252638 | 2 |
| #20243299 | 2 |
| #20241751 | 2 |
| #20241264 | 2 |
| C47×#1471 | 2 |
| #9975 | 47 |