Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#22548741 | C2 | semidirect |
| 2. C2×#22548735 | C2 | semidirect |
| 3. #30632167 | C2 | semidirect |
| 4. #30631906 | C2 | semidirect |
| 5. #30631899 | C2 | semidirect |
| 6. #30631884 | C2 | semidirect |
| 7. #30631879 | C2 | semidirect |
| 8. #30631714 | C2 | semidirect |
| 9. #30631688 | C2 | semidirect |
| 10. C2×#22548636 | C2 | semidirect |
| 11. #535×C251 | C2 | semidirect |
| 15. C2×#16860800 | C22 | semidirect |
| 17. C2×#16860798 | C22 | semidirect |
| 18. C2×#16860797 | C22 | semidirect |
| 20. C2×#16860795 | C22 | semidirect |
| 23. C4×Dic502 | C22 | semidirect |
| 24. C4×D1004 | C22 | semidirect |
| 29. C4⋊(C251⋊C8) | C22 | semidirect |
| 30. C4⋊(C251⋊C8) | C22 | semidirect |
| 31. #22548639 | C22 | semidirect |
| 34. #22548636 | C22 | semidirect |
| 44. #16860810 | D4 | semidirect |
| 154. C251 | #3045 | semidirect |
| 158. #535 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548741 | 2 |
| C2×#22548735 | 2 |
| #30632167 | 2 |
| #30631906 | 2 |
| #30631899 | 2 |
| #30631884 | 2 |
| #30631879 | 2 |
| #30631714 | 2 |
| #30631688 | 2 |
| C2×#22548636 | 2 |
| #535×C251 | 2 |
| #3045 | 251 |