Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
360 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20241383 | C2 | semidirect |
| 5. #20241382 | C2 | semidirect |
| 6. #20241381 | C2 | semidirect |
| 7. C47×#1342 | C2 | semidirect |
| 177. #1342 | D47 | semidirect |
| 202. C47 | #11871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253041 | 2 |
| #20245007 | 2 |
| #20243437 | 2 |
| #20241383 | 2 |
| #20241382 | 2 |
| #20241381 | 2 |
| C47×#1342 | 2 |
| #11871 | 47 |