Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20246353 | C2 | semidirect |
| 5. #20241290 | C2 | semidirect |
| 6. #20241247 | C2 | semidirect |
| 7. C47×#1479 | C2 | semidirect |
| 11. #15689333 | C4 | semidirect |
| 12. #15689323 | C4 | semidirect |
| 196. #1479 | D47 | semidirect |
| 226. C47 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252860 | 2 |
| #20246353 | 2 |
| #20241949 | 2 |
| #20241884 | 2 |
| #20241290 | 2 |
| #20241247 | 2 |
| C47×#1479 | 2 |
| #9182 | 47 |