Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
688 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 215 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. #20243884 | C2 | semidirect |
| 2. #20243863 | C2 | semidirect |
| 3. #20243782 | C2 | semidirect |
| 5. #20243537 | C2 | semidirect |
| 20. C47×#497 | C4 | semidirect |
| 21. C47×#494 | C4 | semidirect |
| 22. C47×#492 | C4 | semidirect |
| 139. #497 | Dic47 | semidirect |
| 140. #494 | Dic47 | semidirect |
| 141. #492 | Dic47 | semidirect |
| 151. C47 | #23360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20243884 | 2 |
| #20243863 | 2 |
| #20243782 | 2 |
| #20243772 | 2 |
| #20243537 | 2 |
| C47×#3152 | 2 |
| #23360 | 47 |