Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
682 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20253901 | C2 | semidirect |
| 3. #20245631 | C2 | semidirect |
| 4. #20245630 | C2 | semidirect |
| 5. #20245629 | C2 | semidirect |
| 6. #20245610 | C2 | semidirect |
| 7. #20245102 | C2 | semidirect |
| 8. #20244981 | C2 | semidirect |
| 9. C47×#2244 | C2 | semidirect |
| 15. #15689527 | C22 | semidirect |
| 16. #15689525 | C22 | semidirect |
| 26. #15688925 | C22 | semidirect |
| 27. #15688924 | C22 | semidirect |
| 28. #15688923 | C22 | semidirect |
| 29. #15688899 | C22 | semidirect |
| 30. C16×Dic47 | C22 | semidirect |
| 31. C47×#499 | C22 | semidirect |
| 33. C47×#357 | C22 | semidirect |
| 34. C47×#346 | C22 | semidirect |
| 156. #2244 | D47 | semidirect |
| 173. #499 | C2×D47 | semidirect |
| 186. #357 | C2×D47 | semidirect |
| 188. #346 | C2×D47 | semidirect |
| 190. C47 | #33704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253901 | 2 |
| #493×D47 | 2 |
| #20245631 | 2 |
| #20245630 | 2 |
| #20245629 | 2 |
| #20245610 | 2 |
| #20245102 | 2 |
| #20244981 | 2 |
| C47×#2244 | 2 |
| #33704 | 47 |