Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×C22⋊#14523339 | C2 | semidirect |
| 3. C2×#22551504 | C2 | semidirect |
| 4. #30656491 | C2 | semidirect |
| 5. C22×M16×C257 | C2 | semidirect |
| 50. C2×C8×C257 | D4 | semidirect |
| 55. C22×D257 | M16 | semidirect |
| 63. C2×Dic257 | M16 | semidirect |
| 113. C257 | #1870 | semidirect |
| 115. C22×M16 | D257 | semidirect |
| 159. C2×C8 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D257 | 2 |
| C2×C22⋊#14523339 | 2 |
| C2×#22551504 | 2 |
| #30656491 | 2 |
| C22×M16×C257 | 2 |
| #1870 | 257 |