Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
456 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 221 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. #30631794 | C2 | semidirect |
| 3. Q16×Dic251 | C2 | semidirect |
| 20. C2×Q16×C251 | C4 | semidirect |
| 72. C251 | #2950 | semidirect |
| 82. C2×Q16 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632165 | 2 |
| #30631794 | 2 |
| Q16×Dic251 | 2 |
| #30631725 | 2 |
| #30631696 | 2 |
| #30631642 | 2 |
| C22×Q16×C251 | 2 |
| #2950 | 251 |