Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
686 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #20241702 | C2 | semidirect |
| 3. #20241319 | C2 | semidirect |
| 4. C47×#1458 | C2 | semidirect |
| 14. #15688849 | C22 | semidirect |
| 18. C47×#324 | C22 | semidirect |
| 26. C22×D188 | C8 | semidirect |
| 176. #1458 | D47 | semidirect |
| 197. #324 | C2×D47 | semidirect |
| 200. C47 | #11433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245968 | 2 |
| #20241702 | 2 |
| #20241319 | 2 |
| C47×#1458 | 2 |
| #11433 | 47 |