Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
404 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20245338 | C2 | semidirect |
| 2. #20245333 | C2 | semidirect |
| 3. #20244492 | C2 | semidirect |
| 4. #20241382 | C2 | semidirect |
| 5. #20241379 | C2 | semidirect |
| 6. #20241326 | C2 | semidirect |
| 7. C47×#3204 | C2 | semidirect |
| 185. #3204 | D47 | semidirect |
| 217. C47 | #12119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245338 | 2 |
| #20245333 | 2 |
| #20244492 | 2 |
| #20241382 | 2 |
| #20241379 | 2 |
| #20241326 | 2 |
| C47×#3204 | 2 |
| #12119 | 47 |