Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C22×#16860795 | C2 | semidirect |
| 2. C2×#22548722 | C2 | semidirect |
| 3. #30632251 | C2 | semidirect |
| 4. #30631938 | C2 | semidirect |
| 5. #30631921 | C2 | semidirect |
| 6. #30631723 | C2 | semidirect |
| 7. #30631692 | C2 | semidirect |
| 8. #30631691 | C2 | semidirect |
| 9. #535×C251 | C2 | semidirect |
| 16. C2×#16860794 | C22 | semidirect |
| 18. C22×C251⋊C8 | C22 | semidirect |
| 21. #22548689 | C22 | semidirect |
| 24. #22548648 | C22 | semidirect |
| 25. #22548646 | C22 | semidirect |
| 26. #22548636 | C22 | semidirect |
| 27. #22548635 | C22 | semidirect |
| 32. #121×C251 | C22 | semidirect |
| 46. C2×C251⋊C8 | D4 | semidirect |
| 125. C251 | #3058 | semidirect |
| 130. #535 | D251 | semidirect |
| 152. #121 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860795 | 2 |
| C2×#22548722 | 2 |
| #30632251 | 2 |
| #30631938 | 2 |
| #30631921 | 2 |
| #30631723 | 2 |
| #30631692 | 2 |
| #30631691 | 2 |
| #535×C251 | 2 |
| #3058 | 251 |