Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
258 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 39 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. #20241509 | C2 | semidirect |
| 2. #20241326 | C2 | semidirect |
| 7. C22×D8×C47 | C4 | semidirect |
| 10. C47×#341 | C4 | semidirect |
| 105. C22×D8 | Dic47 | semidirect |
| 110. #341 | Dic47 | semidirect |
| 111. C47 | #7398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20241509 | 2 |
| #20241326 | 2 |
| C47×#2018 | 2 |
| #7398 | 47 |