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×#15689561 | C2 | semidirect |
| 3. #20253036 | C2 | semidirect |
| 4. #20245336 | C2 | semidirect |
| 5. #20245125 | C2 | semidirect |
| 6. C47×#2115 | C2 | semidirect |
| 12. #15689923 | C22 | semidirect |
| 15. C22×D376 | C22 | semidirect |
| 18. #15689561 | C22 | semidirect |
| 21. #15689376 | C22 | semidirect |
| 23. #15689161 | C22 | semidirect |
| 25. #15688934 | C22 | semidirect |
| 27. C2×M32×C47 | C22 | semidirect |
| 28. C47×#349 | C22 | semidirect |
| 47. #13094046 | D4 | semidirect |
| 50. C2×Dic188 | D4 | semidirect |
| 57. C2×D376 | D4 | semidirect |
| 202. #2115 | D47 | semidirect |
| 224. C2×M32 | C2×D47 | semidirect |
| 230. #349 | 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×#15689561 | 2 |
| #20253036 | 2 |
| #20245336 | 2 |
| #20245125 | 2 |
| C47×#2115 | 2 |
| #33531 | 47 |