Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 20. C2×Dic514 | Q8 | semidirect |
| 73. C257 | #2028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656745 | 2 |
| #30656642 | 2 |
| #30656506 | 2 |
| #30656496 | 2 |
| #544×C257 | 2 |
| #2028 | 257 |