Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#16860799 | C2 | semidirect |
| 2. C2×#22548721 | C2 | semidirect |
| 3. #30632263 | C2 | semidirect |
| 5. #30631934 | C2 | semidirect |
| 6. #30631917 | C2 | semidirect |
| 7. #30631695 | C2 | semidirect |
| 8. #30631691 | C2 | semidirect |
| 9. #427×C251 | C2 | semidirect |
| 18. C2×#16860793 | C22 | semidirect |
| 19. C2×C8×D251 | C22 | semidirect |
| 25. #22548695 | C22 | semidirect |
| 28. #22548638 | C22 | semidirect |
| 33. #107×C251 | C22 | semidirect |
| 34. #106×C251 | C22 | semidirect |
| 62. C2×C8×C251 | D4 | semidirect |
| 120. C251 | #3057 | semidirect |
| 128. #427 | D251 | semidirect |
| 152. #107 | C2×D251 | semidirect |
| 153. #106 | C2×D251 | semidirect |
| 180. C2×C8 | D1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860799 | 2 |
| C2×#22548721 | 2 |
| #30632263 | 2 |
| #30632256 | 2 |
| #30631934 | 2 |
| #30631917 | 2 |
| #30631695 | 2 |
| #30631691 | 2 |
| #427×C251 | 2 |
| #3057 | 251 |