Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
308 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #20241563 | C2 | semidirect |
| 4. #20241548 | C2 | semidirect |
| 12. C47×#541 | C4 | semidirect |
| 15. C47×#494 | C4 | semidirect |
| 16. C47×#491 | C4 | semidirect |
| 22. C47×#433 | C4 | semidirect |
| 148. #541 | Dic47 | semidirect |
| 151. #494 | Dic47 | semidirect |
| 152. #491 | Dic47 | semidirect |
| 158. #433 | Dic47 | semidirect |
| 165. C47 | #13608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245077 | 2 |
| #20245063 | 2 |
| #20241563 | 2 |
| #20241548 | 2 |
| C47×#3223 | 2 |
| #13608 | 47 |