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×#22548740 | C2 | semidirect |
| 2. C22×#16860795 | C2 | semidirect |
| 3. #30632161 | C2 | semidirect |
| 4. #30631899 | C2 | semidirect |
| 5. #30631879 | C2 | semidirect |
| 6. #30631714 | C2 | semidirect |
| 7. #30631692 | C2 | semidirect |
| 8. #30631683 | C2 | semidirect |
| 9. #535×C251 | C2 | semidirect |
| 12. C2×#16860797 | C22 | semidirect |
| 15. C2×#16860795 | C22 | semidirect |
| 18. C4×D1004 | C22 | semidirect |
| 22. C4⋊(C251⋊C8) | C22 | semidirect |
| 23. #22548639 | C22 | semidirect |
| 24. #22548636 | C22 | semidirect |
| 25. #22548636 | C22 | semidirect |
| 28. #127×C251 | C22 | semidirect |
| 29. #124×C251 | C22 | semidirect |
| 36. C2×D1004 | D4 | semidirect |
| 121. C251 | #3041 | semidirect |
| 125. #535 | D251 | semidirect |
| 142. #127 | C2×D251 | semidirect |
| 143. #124 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| C22×#16860795 | 2 |
| #30632161 | 2 |
| #30631899 | 2 |
| #30631879 | 2 |
| #30631714 | 2 |
| #30631692 | 2 |
| #30631683 | 2 |
| #535×C251 | 2 |
| #3041 | 251 |