Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 9. #22548650 | C4 | semidirect |
| 50. C251 | #1778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548650 | 2 |
| M16×Dic251 | 2 |
| C2×#22548625 | 2 |
| #30631452 | 2 |
| #341×C251 | 2 |
| #1778 | 251 |