Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
312 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 16. C2×Q16×C251 | C4 | semidirect |
| 43. C2×Dic251 | Q16 | semidirect |
| 77. C251 | #1969 | semidirect |
| 87. C2×Q16 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548649 | 2 |
| C2×#22548639 | 2 |
| C2×C8×Dic251 | 2 |
| #30631594 | 2 |
| C22×Q16×C251 | 2 |
| #1969 | 251 |