Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30632044 | C2 | semidirect |
| 4. #30631984 | C2 | semidirect |
| 5. #30631969 | C2 | semidirect |
| 6. #30631909 | C2 | semidirect |
| 8. Q8×C251⋊C8 | C2 | semidirect |
| 9. C4×#16860800 | C2 | semidirect |
| 10. C4×#16860797 | C2 | semidirect |
| 11. #557×C251 | C2 | semidirect |
| 117. C251 | #3365 | semidirect |
| 120. #557 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632422 | 2 |
| #30632044 | 2 |
| #30632035 | 2 |
| #30631984 | 2 |
| #30631969 | 2 |
| #30631909 | 2 |
| #30631887 | 2 |
| Q8×C251⋊C8 | 2 |
| C4×#16860800 | 2 |
| C4×#16860797 | 2 |
| #557×C251 | 2 |
| #3365 | 251 |