Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20241817 | C2 | semidirect |
| 5. #20241298 | C2 | semidirect |
| 6. #20241249 | C2 | semidirect |
| 7. C47×#1467 | C2 | semidirect |
| 167. #1467 | D47 | semidirect |
| 196. C47 | #9527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253510 | 2 |
| #20252466 | 2 |
| #20242111 | 2 |
| #20241817 | 2 |
| #20241298 | 2 |
| #20241249 | 2 |
| C47×#1467 | 2 |
| #9527 | 47 |