Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30632242 | C2 | semidirect |
| 3. #30632050 | C2 | semidirect |
| 4. #30632035 | C2 | semidirect |
| 5. #30632034 | C2 | semidirect |
| 6. #30632033 | C2 | semidirect |
| 7. #30631690 | C2 | semidirect |
| 8. C4×#16860793 | C2 | semidirect |
| 9. #486×C251 | C2 | semidirect |
| 14. #22548715 | C22 | semidirect |
| 19. #22548706 | C22 | semidirect |
| 26. #22548637 | C22 | semidirect |
| 27. #22548636 | C22 | semidirect |
| 28. #22548635 | C22 | semidirect |
| 29. #22548625 | C22 | semidirect |
| 30. C4×C251⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C251 | C22 | semidirect |
| 33. #102×C251 | C22 | semidirect |
| 34. C4×C8×C251 | C22 | semidirect |
| 123. C251 | #3138 | semidirect |
| 131. #486 | D251 | semidirect |
| 139. C4⋊Q8 | C2×D251 | semidirect |
| 155. #102 | C2×D251 | semidirect |
| 158. C4×C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| #127×D251 | 2 |
| #30632050 | 2 |
| #30632035 | 2 |
| #30632034 | 2 |
| #30632033 | 2 |
| #30631690 | 2 |
| C4×#16860793 | 2 |
| #486×C251 | 2 |
| #3138 | 251 |