Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20241861 | C2 | semidirect |
| 5. #20241251 | C2 | semidirect |
| 6. #20241217 | C2 | semidirect |
| 7. C47×#1506 | C2 | semidirect |
| 9. #15689526 | C4 | semidirect |
| 10. #15689519 | C4 | semidirect |
| 11. #15689471 | C4 | semidirect |
| 12. #15689471 | C4 | semidirect |
| 166. #1506 | D47 | semidirect |
| 197. C47 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254524 | 2 |
| #20252466 | 2 |
| #20241895 | 2 |
| #20241861 | 2 |
| #20241251 | 2 |
| #20241217 | 2 |
| C47×#1506 | 2 |
| #9279 | 47 |