Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
360 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. #20242171 | C2 | semidirect |
| 5. #20241744 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#1989 | C2 | semidirect |
| 165. #1989 | D47 | semidirect |
| 198. C47 | #10509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254578 | 2 |
| #20242171 | 2 |
| #20242081 | 2 |
| #20241882 | 2 |
| #20241744 | 2 |
| #20241244 | 2 |
| C47×#1989 | 2 |
| #10509 | 47 |