Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 183 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. #20258162 | C2 | semidirect |
| 2. C2×#15689559 | C2 | semidirect |
| 3. #20245333 | C2 | semidirect |
| 4. #20245123 | C2 | semidirect |
| 5. #20245009 | C2 | semidirect |
| 6. C47×#3058 | C2 | semidirect |
| 12. #15689923 | C22 | semidirect |
| 16. #15689559 | C22 | semidirect |
| 19. C2×#13093964 | C22 | semidirect |
| 20. #15688932 | C22 | semidirect |
| 21. #15688905 | C22 | semidirect |
| 22. C22×D8×C47 | C22 | semidirect |
| 25. C47×#469 | C22 | semidirect |
| 27. C47×#427 | C22 | semidirect |
| 46. #13094046 | D4 | semidirect |
| 49. C2×Dic188 | D4 | semidirect |
| 53. C2×D376 | D4 | semidirect |
| 199. #3058 | D47 | semidirect |
| 217. C22×D8 | C2×D47 | semidirect |
| 225. #469 | C2×D47 | semidirect |
| 227. #427 | C2×D47 | semidirect |
| 231. C47 | #33531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20258162 | 2 |
| C2×#15689559 | 2 |
| #20245333 | 2 |
| #20245123 | 2 |
| #20245009 | 2 |
| C47×#3058 | 2 |
| #33531 | 47 |