Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic2056 | C2 | semidirect |
| 3. C2×#22551536 | C2 | semidirect |
| 4. #30656979 | C2 | semidirect |
| 5. #30656540 | C2 | semidirect |
| 6. #30656516 | C2 | semidirect |
| 7. #357×C257 | C2 | semidirect |
| 85. C257 | #2189 | semidirect |
| 92. #357 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551611 | 2 |
| C2×Dic2056 | 2 |
| C2×#22551536 | 2 |
| #30656979 | 2 |
| #30656540 | 2 |
| #30656516 | 2 |
| #357×C257 | 2 |
| #2189 | 257 |