Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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×D4×Dic257 | C2 | semidirect |
| 3. C2×#22551554 | C2 | semidirect |
| 4. #30656639 | C2 | semidirect |
| 5. #30656614 | C2 | semidirect |
| 6. #30656613 | C2 | semidirect |
| 7. #30656602 | C2 | semidirect |
| 8. #30656583 | C2 | semidirect |
| 9. #390×C257 | C2 | semidirect |
| 14. #22551588 | C4 | semidirect |
| 33. C2×D1028 | C2×C4 | semidirect |
| 36. C2×C22⋊D257 | C2×C4 | semidirect |
| 49. C4×Dic257 | C2×C4 | semidirect |
| 50. C4×Dic257 | D4 | semidirect |
| 54. C2×D4×C257 | C2×C4 | semidirect |
| 123. C257 | #2328 | semidirect |
| 129. #390 | D257 | semidirect |
| 164. C2×D4 | C4×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551588 | 2 |
| C2×D4×Dic257 | 2 |
| C2×#22551554 | 2 |
| #30656639 | 2 |
| #30656614 | 2 |
| #30656613 | 2 |
| #30656602 | 2 |
| #30656583 | 2 |
| #390×C257 | 2 |
| #2328 | 257 |