Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #30631712 | C2 | semidirect |
| 4. #30631711 | C2 | semidirect |
| 5. #30631710 | C2 | semidirect |
| 6. #423×C251 | C2 | semidirect |
| 17. C4⋊(C251⋊C8) | C22 | semidirect |
| 18. Dic251⋊C8 | C22 | semidirect |
| 21. C4⋊C8×C251 | C22 | semidirect |
| 78. C251 | #2905 | semidirect |
| 85. #423 | D251 | semidirect |
| 100. 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×M16×D251 | 2 |
| C2×#22548672 | 2 |
| #30631712 | 2 |
| #30631711 | 2 |
| #30631710 | 2 |
| #423×C251 | 2 |
| #2905 | 251 |