Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
304 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 304 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. #20245204 | C2 | semidirect |
| 2. #20243143 | C2 | semidirect |
| 3. #20241382 | C2 | semidirect |
| 5. #20241376 | C2 | semidirect |
| 17. C47×#498 | C4 | semidirect |
| 18. C47×#495 | C4 | semidirect |
| 23. C47×#442 | C4 | semidirect |
| 24. C47×#441 | C4 | semidirect |
| 153. #498 | Dic47 | semidirect |
| 154. #495 | Dic47 | semidirect |
| 159. #442 | Dic47 | semidirect |
| 160. #441 | Dic47 | semidirect |
| 171. C47 | #11769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245204 | 2 |
| #20243143 | 2 |
| #20241382 | 2 |
| #20241379 | 2 |
| #20241376 | 2 |
| #20241373 | 2 |
| C47×#3173 | 2 |
| #11769 | 47 |