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×#22548723 | C2 | semidirect |
| 2. #30632265 | C2 | semidirect |
| 3. #30632254 | C2 | semidirect |
| 4. #30631937 | C2 | semidirect |
| 5. #30631930 | C2 | semidirect |
| 6. #30631920 | C2 | semidirect |
| 7. #30631913 | C2 | semidirect |
| 8. #30631729 | C2 | semidirect |
| 9. #30631683 | C2 | semidirect |
| 10. C2×#22548636 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C251 | C2 | semidirect |
| 14. C2×#16860793 | C22 | semidirect |
| 16. C2×C8×D251 | C22 | semidirect |
| 20. #22548691 | C22 | semidirect |
| 25. #22548686 | C22 | semidirect |
| 29. #22548649 | C22 | semidirect |
| 30. #22548647 | C22 | semidirect |
| 31. #22548639 | C22 | semidirect |
| 32. #22548639 | C22 | semidirect |
| 35. #22548636 | C22 | semidirect |
| 36. #22548636 | C22 | semidirect |
| 83. M16×C251 | D4 | semidirect |
| 151. C251 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D251 | semidirect |
| 220. M16 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548723 | 2 |
| #30632265 | 2 |
| #30632254 | 2 |
| #30631937 | 2 |
| #30631930 | 2 |
| #30631920 | 2 |
| #30631913 | 2 |
| #30631729 | 2 |
| #30631683 | 2 |
| C2×#22548636 | 2 |
| C2×AGL(1,ℤ/8)×C251 | 2 |
| #3062 | 251 |