Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 11. #22551591 | C4 | semidirect |
| 35. C4⋊Dic257 | Q8 | semidirect |
| 49. C4⋊C4×C257 | Q8 | semidirect |
| 102. C257 | #1988 | semidirect |
| 149. C4⋊C4 | Dic514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551591 | 2 |
| C2×#22551521 | 2 |
| C4⋊C4×Dic257 | 2 |
| #30656500 | 2 |
| #30656499 | 2 |
| #340×C257 | 2 |
| #1988 | 257 |