Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
260 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 23. C4⋊Dic257 | C8 | semidirect |
| 67. C4×C257 | C4⋊C8 | semidirect |
| 81. C257 | #1939 | semidirect |
| 151. C4 | #22551521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#14523339 | 2 |
| C2×#22551521 | 2 |
| C4×C4⋊Dic257 | 2 |
| #30656491 | 2 |
| C2×C4×C8×C257 | 2 |
| #1939 | 257 |