Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 159 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. #499×D47 | C2 | semidirect |
| 3. #20245631 | C2 | semidirect |
| 4. #20245630 | C2 | semidirect |
| 5. #20245629 | C2 | semidirect |
| 6. #20245628 | C2 | semidirect |
| 7. #357×D47 | C2 | semidirect |
| 8. #346×D47 | C2 | semidirect |
| 9. C47×#2244 | C2 | semidirect |
| 15. #15689525 | C22 | semidirect |
| 16. #15689524 | C22 | semidirect |
| 26. #15688925 | C22 | semidirect |
| 27. #15688924 | C22 | semidirect |
| 28. #15688923 | C22 | semidirect |
| 29. #15688899 | C22 | semidirect |
| 30. #15688898 | C22 | semidirect |
| 31. C47×#499 | C22 | semidirect |
| 33. C47×#357 | C22 | semidirect |
| 34. C47×#346 | C22 | semidirect |
| 157. #2244 | D47 | direct (N × H) |
| 164. D47 | #2244 | direct (N × H) |
| 174. #499 | C2×D47 | semidirect |
| 186. #357 | C2×D47 | semidirect |
| 189. #346 | C2×D47 | semidirect |
| 190. C47 | C2×#2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D47 | 2 |
| #493×D47 | 2 |
| #20245631 | 2 |
| #20245630 | 2 |
| #20245629 | 2 |
| #20245628 | 2 |
| #357×D47 | 2 |
| #346×D47 | 2 |
| C47×#2244 | 2 |
| C2×#2244 | 47 |