Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20256541 | C2 | semidirect |
| 2. #20256529 | C2 | semidirect |
| 3. #20245708 | C2 | semidirect |
| 4. #20245703 | C2 | semidirect |
| 5. #20245697 | C2 | semidirect |
| 6. C2×#15688962 | C2 | semidirect |
| 7. C47×#2258 | C2 | semidirect |
| 13. #15689555 | C22 | semidirect |
| 14. C2×Dic376 | C22 | semidirect |
| 16. Dic752 | C22 | semidirect |
| 17. #15688962 | C22 | semidirect |
| 18. #15688962 | C22 | semidirect |
| 19. #15688962 | C22 | semidirect |
| 20. D1504 | C22 | semidirect |
| 22. C47×M64 | C22 | semidirect |
| 23. C2×C32×C47 | C22 | semidirect |
| 98. #2258 | D47 | semidirect |
| 117. M64 | C2×D47 | semidirect |
| 118. C2×C32 | C2×D47 | semidirect |
| 119. C47 | #33983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256541 | 2 |
| #20256529 | 2 |
| #20245708 | 2 |
| #20245703 | 2 |
| #20245697 | 2 |
| C2×#15688962 | 2 |
| C47×#2258 | 2 |
| #33983 | 47 |