Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 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. #20241809 | C2 | semidirect |
| 5. #20241252 | C2 | semidirect |
| 6. #20241251 | C2 | semidirect |
| 7. C47×#1515 | C2 | semidirect |
| 9. #15689529 | C4 | semidirect |
| 10. #15689529 | C4 | semidirect |
| 11. #15689485 | C4 | semidirect |
| 12. #15689485 | C4 | semidirect |
| 188. #1515 | D47 | semidirect |
| 224. C47 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254628 | 2 |
| #20252368 | 2 |
| #20241963 | 2 |
| #20241809 | 2 |
| #20241252 | 2 |
| #20241251 | 2 |
| C47×#1515 | 2 |
| #9369 | 47 |