Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
682 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×Dic376 | C2 | semidirect |
| 4. #20245497 | C2 | direct (N × H) |
| 5. C2×#15688926 | C2 | semidirect |
| 6. C2×C47×#367 | C2 | semidirect |
| 11. C2×Dic376 | C22 | semidirect |
| 18. #15688926 | C22 | semidirect |
| 21. C47×#367 | C22 | semidirect |
| 120. C2×#367 | D47 | semidirect |
| 122. C2×C47 | #2219 | semidirect |
| 139. #367 | C2×D47 | semidirect |
| 141. C47 | C2×#2219 | semidirect |
| 236. C2 | #20245497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic376 | 2 |
| C22×#13093963 | 2 |
| C2×#15689365 | 2 |
| #20245497 | 2 |
| C2×#15688926 | 2 |
| C2×C47×#367 | 2 |
| C2×#2219 | 47 |