Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22548743 | C2 | semidirect |
| 2. C22×D2008 | C2 | semidirect |
| 3. #30632256 | C2 | semidirect |
| 4. #30632161 | C2 | semidirect |
| 5. #30631903 | C2 | semidirect |
| 6. #30631883 | C2 | semidirect |
| 7. #30631693 | C2 | semidirect |
| 8. #30631684 | C2 | semidirect |
| 9. #424×C251 | C2 | semidirect |
| 14. C2×#16860799 | C22 | semidirect |
| 17. C2×D2008 | C22 | semidirect |
| 18. #22548712 | C22 | semidirect |
| 19. #22548703 | C22 | semidirect |
| 22. C4×D1004 | C22 | semidirect |
| 26. #22548640 | C22 | semidirect |
| 27. #22548637 | C22 | semidirect |
| 28. #22548637 | C22 | semidirect |
| 32. C4⋊C8×C251 | C22 | semidirect |
| 44. C2×D1004 | D4 | semidirect |
| 121. C251 | #3041 | semidirect |
| 129. #424 | D251 | semidirect |
| 151. C4⋊C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548743 | 2 |
| C22×D2008 | 2 |
| #30632256 | 2 |
| #30632161 | 2 |
| #30631903 | 2 |
| #30631883 | 2 |
| #30631693 | 2 |
| #30631684 | 2 |
| #424×C251 | 2 |
| #3041 | 251 |