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. #20241518 | C2 | semidirect |
| 6. #20241517 | C2 | semidirect |
| 7. C47×#1858 | C2 | semidirect |
| 20. #15688921 | C4 | semidirect |
| 21. #15688919 | C4 | semidirect |
| 186. #1858 | D47 | semidirect |
| 216. C47 | #12975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252452 | 2 |
| #20245071 | 2 |
| #20243771 | 2 |
| #20243608 | 2 |
| #20241518 | 2 |
| #20241517 | 2 |
| C47×#1858 | 2 |
| #12975 | 47 |