Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #30632523 | C2 | semidirect |
| 2. C2×#22548762 | C2 | semidirect |
| 3. #30632504 | C2 | semidirect |
| 4. #30632499 | C2 | semidirect |
| 5. #30632487 | C2 | semidirect |
| 6. C2×#22548748 | C2 | semidirect |
| 7. #568×C251 | C2 | semidirect |
| 10. #22548762 | C22 | semidirect |
| 11. #22548762 | C22 | semidirect |
| 12. #22548761 | C22 | semidirect |
| 15. C2×#16860810 | C22 | semidirect |
| 18. C22×Dic502 | C22 | semidirect |
| 20. #22548748 | C22 | semidirect |
| 21. #22548748 | C22 | semidirect |
| 22. #22548748 | C22 | semidirect |
| 23. #22548743 | C22 | semidirect |
| 24. #22548743 | C22 | semidirect |
| 25. #22548737 | C22 | semidirect |
| 26. C2×Dic1004 | C22 | semidirect |
| 27. C2×#16860799 | C22 | semidirect |
| 29. #131×C251 | C22 | semidirect |
| 30. C2×M16×C251 | C22 | semidirect |
| 112. C251 | #3586 | semidirect |
| 120. #568 | D251 | semidirect |
| 142. #131 | C2×D251 | semidirect |
| 143. C2×M16 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632523 | 2 |
| C2×#22548762 | 2 |
| #30632504 | 2 |
| #30632499 | 2 |
| #30632487 | 2 |
| C2×#22548748 | 2 |
| #568×C251 | 2 |
| #3586 | 251 |