Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
462 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20241990 | C2 | semidirect |
| 5. #20241252 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#2336 | C2 | semidirect |
| 9. #15689533 | C4 | semidirect |
| 10. #15689489 | C4 | semidirect |
| 193. #2336 | D47 | semidirect |
| 228. C47 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254578 | 2 |
| #20244306 | 2 |
| #20241990 | 2 |
| #20241934 | 2 |
| #20241252 | 2 |
| #20241244 | 2 |
| C47×#2336 | 2 |
| #9382 | 47 |