Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. #30631983 | C2 | semidirect |
| 5. #30631982 | C2 | semidirect |
| 6. #30631894 | C2 | semidirect |
| 8. Q16×Dic251 | C2 | semidirect |
| 9. #30631779 | C2 | semidirect |
| 11. #462×C251 | C2 | semidirect |
| 98. C4×D251 | Q16 | semidirect |
| 132. C251 | #3104 | semidirect |
| 140. #462 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| C4×Q8×D251 | 2 |
| #30632021 | 2 |
| #30631983 | 2 |
| #30631982 | 2 |
| #30631894 | 2 |
| #30631841 | 2 |
| Q16×Dic251 | 2 |
| #30631779 | 2 |
| #30631739 | 2 |
| #462×C251 | 2 |
| #3104 | 251 |