Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20243608 | C2 | semidirect |
| 5. #20241516 | C2 | semidirect |
| 6. #20241511 | C2 | semidirect |
| 7. C47×#1868 | C2 | semidirect |
| 187. #1868 | D47 | semidirect |
| 218. C47 | #12963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252446 | 2 |
| #20245027 | 2 |
| #20243806 | 2 |
| #20243608 | 2 |
| #20241516 | 2 |
| #20241511 | 2 |
| C47×#1868 | 2 |
| #12963 | 47 |