Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
410 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20254278 | C2 | semidirect |
| 2. #20245317 | C2 | semidirect |
| 4. #20241407 | C2 | semidirect |
| 5. #20241406 | C2 | semidirect |
| 6. #20241313 | C2 | semidirect |
| 7. C47×#2187 | C2 | semidirect |
| 175. #2187 | D47 | semidirect |
| 205. C47 | #12109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254278 | 2 |
| #20245317 | 2 |
| #20244495 | 2 |
| #20241407 | 2 |
| #20241406 | 2 |
| #20241313 | 2 |
| C47×#2187 | 2 |
| #12109 | 47 |