Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #30632485 | C2 | semidirect |
| 2. C2×#22548741 | C2 | semidirect |
| 3. #30632454 | C2 | semidirect |
| 4. #30631955 | C2 | semidirect |
| 5. #30631948 | C2 | semidirect |
| 6. #30631735 | C2 | semidirect |
| 7. #30631669 | C2 | semidirect |
| 8. C2×#22548632 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C251 | C2 | semidirect |
| 12. #22548745 | C22 | semidirect |
| 16. #22548740 | C22 | semidirect |
| 18. C2×#16860798 | C22 | semidirect |
| 19. C2×#16860795 | C22 | semidirect |
| 21. #22548722 | C22 | semidirect |
| 26. #22548650 | C22 | semidirect |
| 27. #22548633 | C22 | semidirect |
| 28. #22548632 | C22 | semidirect |
| 29. #22548631 | C22 | semidirect |
| 147. C251 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632485 | 2 |
| C2×#22548741 | 2 |
| #30632454 | 2 |
| #30631955 | 2 |
| #30631948 | 2 |
| #30631735 | 2 |
| #30631669 | 2 |
| C2×#22548632 | 2 |
| C2×AGL(1,ℤ/8)×C251 | 2 |
| #3068 | 251 |