Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 133 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. #30632522 | C2 | semidirect |
| 2. #30632195 | C2 | semidirect |
| 3. #30631876 | C2 | semidirect |
| 4. #30631875 | C2 | semidirect |
| 5. #30631874 | C2 | semidirect |
| 6. #30631659 | C2 | semidirect |
| 7. #458×C251 | C2 | semidirect |
| 14. C22×C4×D251 | C22 | semidirect |
| 15. #22548698 | C22 | semidirect |
| 18. #22548685 | C22 | semidirect |
| 19. #22548683 | C22 | semidirect |
| 22. #22548671 | C22 | semidirect |
| 23. #22548630 | C22 | semidirect |
| 24. #22548629 | C22 | semidirect |
| 26. #123×C251 | C22 | semidirect |
| 27. #99×C251 | C22 | semidirect |
| 38. C2×Dic502 | D4 | semidirect |
| 44. C2×C22⋊D251 | D4 | semidirect |
| 49. C22×Dic251 | D4 | semidirect |
| 54. C2×C4×D251 | D4 | semidirect |
| 126. C251 | #3025 | semidirect |
| 131. #458 | D251 | semidirect |
| 144. #123 | C2×D251 | semidirect |
| 154. #99 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632522 | 2 |
| #30632195 | 2 |
| #30631876 | 2 |
| #30631875 | 2 |
| #30631874 | 2 |
| #30631659 | 2 |
| #458×C251 | 2 |
| #3025 | 251 |