Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#15689566 | C2 | semidirect |
| 2. C22×#13093968 | C2 | semidirect |
| 4. #20252255 | C2 | semidirect |
| 5. #20245449 | C2 | semidirect |
| 6. #20245427 | C2 | semidirect |
| 7. #20245148 | C2 | semidirect |
| 8. #20245093 | C2 | semidirect |
| 9. C47×#2140 | C2 | semidirect |
| 16. C2×Dic376 | C22 | semidirect |
| 17. C2×#13093969 | C22 | semidirect |
| 25. #15689217 | C22 | semidirect |
| 28. Dic47⋊C16 | C22 | semidirect |
| 29. #15688926 | C22 | semidirect |
| 30. #15688923 | C22 | semidirect |
| 42. C2×Dic188 | D4 | semidirect |
| 179. #2140 | D47 | semidirect |
| 211. C47 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689566 | 2 |
| C22×#13093968 | 2 |
| #20253869 | 2 |
| #20252255 | 2 |
| #20245449 | 2 |
| #20245427 | 2 |
| #20245148 | 2 |
| #20245093 | 2 |
| C47×#2140 | 2 |
| #33587 | 47 |