Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1244 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 1. #20252520 | C2 | semidirect |
| 2. #20242123 | C2 | semidirect |
| 3. #20242056 | C2 | semidirect |
| 4. #20242050 | C2 | semidirect |
| 8. #15689176 | C22 | semidirect |
| 9. #15689147 | C22 | semidirect |
| 10. #15688872 | C22 | semidirect |
| 11. #15688872 | C22 | semidirect |
| 12. #15688867 | C22 | semidirect |
| 13. #15688867 | C22 | semidirect |
| 137. C47 | #17782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252520 | 2 |
| #20242123 | 2 |
| #20242056 | 2 |
| #20242050 | 2 |
| C47×#3498 | 2 |
| #17782 | 47 |