Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20254047 | C2 | semidirect |
| 3. #20245608 | C2 | semidirect |
| 4. #20245565 | C2 | semidirect |
| 5. #20245470 | C2 | semidirect |
| 7. #20245281 | C2 | semidirect |
| 8. C47×#2166 | C2 | semidirect |
| 13. #15689525 | C22 | semidirect |
| 14. #15689503 | C22 | semidirect |
| 22. #15689231 | C22 | semidirect |
| 26. #15688946 | C22 | semidirect |
| 27. #15688940 | C22 | semidirect |
| 30. C47×#364 | C22 | semidirect |
| 32. C47×#347 | C22 | semidirect |
| 164. #2166 | D47 | semidirect |
| 188. #364 | C2×D47 | semidirect |
| 192. #347 | C2×D47 | semidirect |
| 193. C47 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254047 | 2 |
| #20252292 | 2 |
| #20245608 | 2 |
| #20245565 | 2 |
| #20245470 | 2 |
| #20245341 | 2 |
| #20245281 | 2 |
| C47×#2166 | 2 |
| #33693 | 47 |