Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 24. C2×Q16×C257 | C4 | semidirect |
| 71. C2×Dic257 | Q16 | semidirect |
| 119. C257 | #1878 | semidirect |
| 132. C2×Q16 | Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic257 | 2 |
| C2×#22551516 | 2 |
| #30656644 | 2 |
| #30656500 | 2 |
| #30656491 | 2 |
| C22×Q16×C257 | 2 |
| #1878 | 257 |