Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
346 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20254789 | C2 | semidirect |
| 2. #20245339 | C2 | semidirect |
| 4. #20241381 | C2 | semidirect |
| 5. #20241378 | C2 | semidirect |
| 6. #20241339 | C2 | semidirect |
| 7. C47×#2050 | C2 | semidirect |
| 169. #2050 | D47 | semidirect |
| 197. C47 | #12175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254789 | 2 |
| #20245339 | 2 |
| #20245334 | 2 |
| #20241381 | 2 |
| #20241378 | 2 |
| #20241339 | 2 |
| C47×#2050 | 2 |
| #12175 | 47 |