Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
450 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20241982 | C2 | semidirect |
| 5. #20241901 | C2 | semidirect |
| 6. #20241280 | C2 | semidirect |
| 7. C47×#1291 | C2 | semidirect |
| 11. #15689419 | C4 | semidirect |
| 12. #15689414 | C4 | semidirect |
| 13. #15689334 | C4 | semidirect |
| 14. #15689329 | C4 | semidirect |
| 196. #1291 | D47 | semidirect |
| 227. C47 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253551 | 2 |
| #20252405 | 2 |
| #20243201 | 2 |
| #20241982 | 2 |
| #20241901 | 2 |
| #20241280 | 2 |
| C47×#1291 | 2 |
| #9160 | 47 |