Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #30631785 | C2 | semidirect |
| 4. C4×#16860797 | C2 | semidirect |
| 5. #30631723 | C2 | semidirect |
| 6. #30631696 | C2 | semidirect |
| 8. #30631643 | C2 | semidirect |
| 9. #519×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | semidirect |
| 20. #22548648 | C22 | semidirect |
| 21. #22548646 | C22 | semidirect |
| 22. #22548639 | C22 | semidirect |
| 24. #22548626 | C22 | semidirect |
| 25. C4×C251⋊C8 | C22 | semidirect |
| 28. C4×Q8×C251 | C22 | semidirect |
| 38. #16860797 | C2×C4 | semidirect |
| 39. #16860797 | C2×C4 | semidirect |
| 41. C2×C251⋊C8 | C2×C4 | semidirect |
| 51. C2×Q8×C251 | C2×C4 | semidirect |
| 103. C251 | #2949 | semidirect |
| 106. #519 | D251 | semidirect |
| 122. C4×Q8 | C2×D251 | semidirect |
| 139. C2×Q8 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| #30632161 | 2 |
| #30631785 | 2 |
| C4×#16860797 | 2 |
| #30631723 | 2 |
| #30631696 | 2 |
| #30631691 | 2 |
| #30631643 | 2 |
| #519×C251 | 2 |
| #2949 | 251 |