Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
218 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20245296 | C2 | semidirect |
| 4. #20241458 | C2 | semidirect |
| 5. #20241368 | C2 | semidirect |
| 7. C47×#1312 | C2 | semidirect |
| 84. C8×C47 | M32 | semidirect |
| 108. #1312 | D47 | semidirect |
| 128. C47 | #12058 | semidirect |
| 192. C8 | #13093963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245296 | 2 |
| #20245221 | 2 |
| C8×#10625325 | 2 |
| #20241458 | 2 |
| #20241368 | 2 |
| #20241344 | 2 |
| C47×#1312 | 2 |
| #12058 | 47 |