Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
666 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20251865 | C2 | semidirect |
| 3. #20245038 | C2 | semidirect |
| 4. #20243359 | C2 | semidirect |
| 5. #20241518 | C2 | semidirect |
| 6. #20241510 | C2 | semidirect |
| 7. C47×#2134 | C2 | semidirect |
| 9. C2×#13094050 | C4 | semidirect |
| 10. C22×#10625334 | C4 | semidirect |
| 18. #15689127 | C4 | semidirect |
| 19. #15689117 | C4 | semidirect |
| 249. #2134 | D47 | semidirect |
| 286. C47 | #13099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252654 | 2 |
| #20251865 | 2 |
| #20245038 | 2 |
| #20243359 | 2 |
| #20241518 | 2 |
| #20241510 | 2 |
| C47×#2134 | 2 |
| #13099 | 47 |