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. C2×#22548762 | C2 | semidirect |
| 2. #30632502 | C2 | semidirect |
| 3. #30632498 | C2 | semidirect |
| 4. #30632485 | C2 | semidirect |
| 5. C2×#22548745 | C2 | semidirect |
| 6. #30632454 | C2 | semidirect |
| 7. #585×C251 | C2 | semidirect |
| 9. #22548762 | C22 | semidirect |
| 10. C2×#16860810 | C22 | semidirect |
| 12. C22×Dic502 | C22 | semidirect |
| 14. #22548746 | C22 | semidirect |
| 15. #22548745 | C22 | semidirect |
| 16. #22548745 | C22 | semidirect |
| 17. #22548741 | C22 | semidirect |
| 18. #22548740 | C22 | semidirect |
| 19. #22548735 | C22 | semidirect |
| 20. C2×#16860800 | C22 | semidirect |
| 21. C2×#16860798 | C22 | semidirect |
| 22. #22548722 | C22 | semidirect |
| 23. C2×#16860794 | C22 | semidirect |
| 25. 2−1+4×C251 | C22 | semidirect |
| 27. H(5,𝔽2)×C251 | C22 | semidirect |
| 112. C251 | #3586 | semidirect |
| 114. #585 | D251 | semidirect |
| 124. 2−1+4 | C2×D251 | semidirect |
| 126. H(5,𝔽2) | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548762 | 2 |
| #30632502 | 2 |
| #30632498 | 2 |
| #30632485 | 2 |
| C2×#22548745 | 2 |
| #30632454 | 2 |
| #585×C251 | 2 |
| #3586 | 251 |