Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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. #20243674 | C2 | semidirect |
| 5. #20241509 | C2 | semidirect |
| 6. #20241508 | C2 | semidirect |
| 7. C47×#1868 | C2 | semidirect |
| 20. #15688917 | C4 | semidirect |
| 21. #15688915 | C4 | semidirect |
| 188. #1868 | D47 | semidirect |
| 218. C47 | #12968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252452 | 2 |
| #20245051 | 2 |
| #20243771 | 2 |
| #20243674 | 2 |
| #20241509 | 2 |
| #20241508 | 2 |
| C47×#1868 | 2 |
| #12968 | 47 |