Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
344 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 1. #20245080 | C2 | semidirect |
| 2. #20245057 | C2 | semidirect |
| 3. #20241563 | C2 | semidirect |
| 4. #20241545 | C2 | semidirect |
| 12. C47×#540 | C4 | semidirect |
| 15. C47×#493 | C4 | semidirect |
| 16. C47×#490 | C4 | semidirect |
| 22. C47×#433 | C4 | semidirect |
| 36. #127×C47 | C2×C4 | semidirect |
| 38. #125×C47 | C2×C4 | semidirect |
| 54. #97×C47 | C2×C4 | semidirect |
| 55. C4×C8×C47 | C2×C4 | semidirect |
| 164. #540 | Dic47 | semidirect |
| 167. #493 | Dic47 | semidirect |
| 168. #490 | Dic47 | semidirect |
| 174. #433 | Dic47 | semidirect |
| 181. C47 | #13605 | semidirect |
| 190. #127 | C2×Dic47 | semidirect |
| 192. #125 | C2×Dic47 | semidirect |
| 213. #97 | C2×Dic47 | semidirect |
| 214. C4×C8 | C2×Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245080 | 2 |
| #20245057 | 2 |
| #20241563 | 2 |
| #20241545 | 2 |
| C47×#3220 | 2 |
| #13605 | 47 |