Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic514 | C2 | semidirect |
| 3. #30656642 | C2 | semidirect |
| 5. #30656625 | C2 | semidirect |
| 6. #30656610 | C2 | semidirect |
| 7. #30656606 | C2 | semidirect |
| 8. #30656583 | C2 | semidirect |
| 11. #22551579 | C4 | semidirect |
| 32. C2×Dic514 | C2×C4 | semidirect |
| 41. C22⋊Dic257 | C2×C4 | semidirect |
| 44. C4×Dic257 | C2×C4 | semidirect |
| 111. C257 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551579 | 2 |
| C2×C4×Dic514 | 2 |
| #30656642 | 2 |
| #30656640 | 2 |
| #30656625 | 2 |
| #30656610 | 2 |
| #30656606 | 2 |
| #30656583 | 2 |
| C2×C4×D4×C257 | 2 |
| #2326 | 257 |