Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 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. #20241809 | C2 | semidirect |
| 5. #20241287 | C2 | semidirect |
| 6. #20241261 | C2 | semidirect |
| 7. C47×#1531 | C2 | semidirect |
| 179. #1531 | D47 | semidirect |
| 212. C47 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253544 | 2 |
| #20252037 | 2 |
| #20241820 | 2 |
| #20241809 | 2 |
| #20241287 | 2 |
| #20241261 | 2 |
| C47×#1531 | 2 |
| #9314 | 47 |