Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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. #30631743 | C2 | semidirect |
| 3. #30631739 | C2 | semidirect |
| 4. #30631711 | C2 | semidirect |
| 6. M16×Dic251 | C2 | semidirect |
| 7. #423×C251 | C2 | semidirect |
| 17. C4⋊(C251⋊C8) | C22 | semidirect |
| 19. #22548625 | C22 | semidirect |
| 20. C8×Dic251 | C22 | semidirect |
| 23. C4⋊C8×C251 | C22 | semidirect |
| 66. C4×D251 | M16 | semidirect |
| 96. C251 | #2920 | semidirect |
| 102. #423 | D251 | semidirect |
| 117. C4⋊C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D251 | 2 |
| #30631743 | 2 |
| #30631739 | 2 |
| #30631711 | 2 |
| #30631650 | 2 |
| M16×Dic251 | 2 |
| #423×C251 | 2 |
| #2920 | 251 |