Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 2. #20252448 | C2 | semidirect |
| 3. #20241945 | C2 | semidirect |
| 4. #20241917 | C2 | semidirect |
| 5. #20241297 | C2 | semidirect |
| 6. #20241265 | C2 | semidirect |
| 7. C47×#1471 | C2 | semidirect |
| 9. #15689453 | C4 | semidirect |
| 11. #15689436 | C4 | semidirect |
| 14. #15689274 | C4 | semidirect |
| 16. #15689257 | C4 | semidirect |
| 222. #1471 | D47 | semidirect |
| 260. C47 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254202 | 2 |
| #20252448 | 2 |
| #20241945 | 2 |
| #20241917 | 2 |
| #20241297 | 2 |
| #20241265 | 2 |
| C47×#1471 | 2 |
| #9332 | 47 |