Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
408 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20245070 | C2 | semidirect |
| 3. #20245052 | C2 | semidirect |
| 4. #20241548 | C2 | semidirect |
| 5. #20241546 | C2 | semidirect |
| 6. #20241544 | C2 | semidirect |
| 7. C47×#1407 | C2 | semidirect |
| 10. #15689674 | C4 | semidirect |
| 13. #15689515 | C4 | semidirect |
| 15. #15689512 | C4 | semidirect |
| 19. #97×D47 | C4 | semidirect |
| 182. #1407 | D47 | semidirect |
| 210. C47 | #13577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253832 | 2 |
| #20245070 | 2 |
| #20245052 | 2 |
| #20241548 | 2 |
| #20241546 | 2 |
| #20241544 | 2 |
| C47×#1407 | 2 |
| #13577 | 47 |