Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #30631760 | C2 | semidirect |
| 3. #30631757 | C2 | semidirect |
| 4. C8×D1004 | C2 | semidirect |
| 5. #30631752 | C2 | semidirect |
| 6. #30631748 | C2 | semidirect |
| 7. #30631652 | C2 | semidirect |
| 8. C22⋊C8×D251 | C2 | semidirect |
| 9. #433×C251 | C2 | semidirect |
| 12. C2×#16860793 | C22 | semidirect |
| 15. C2×C8×D251 | C22 | semidirect |
| 22. C4⋊(C251⋊C8) | C22 | semidirect |
| 26. (C2×D251)⋊C8 | C22 | semidirect |
| 27. (C2×D251)⋊C8 | C22 | semidirect |
| 28. #22548626 | C22 | semidirect |
| 29. C4×C251⋊C8 | C22 | semidirect |
| 31. C4⋊C8×C251 | C22 | semidirect |
| 33. #97×C251 | C22 | semidirect |
| 34. C4×C8×C251 | C22 | semidirect |
| 114. C251 | #2977 | semidirect |
| 122. #433 | D251 | semidirect |
| 139. C4⋊C8 | C2×D251 | semidirect |
| 147. #97 | C2×D251 | semidirect |
| 149. C4×C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632199 | 2 |
| #30631760 | 2 |
| #30631757 | 2 |
| C8×D1004 | 2 |
| #30631752 | 2 |
| #30631748 | 2 |
| #30631652 | 2 |
| C22⋊C8×D251 | 2 |
| #433×C251 | 2 |
| #2977 | 251 |