Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C2×#22551526 | C2 | semidirect |
| 2. C2×#22551513 | C2 | semidirect |
| 3. C2×C8×Dic257 | C2 | semidirect |
| 4. #30656640 | C2 | semidirect |
| 16. C2×D8×C257 | C4 | semidirect |
| 44. C2×Dic257 | D8 | semidirect |
| 62. C8×C257 | C22⋊C4 | semidirect |
| 85. C257 | #1970 | semidirect |
| 95. C2×D8 | Dic257 | semidirect |
| 148. C8 | C22⋊Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551526 | 2 |
| C2×#22551513 | 2 |
| C2×C8×Dic257 | 2 |
| #30656640 | 2 |
| C22×D8×C257 | 2 |
| #1970 | 257 |