Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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. #30656631 | C2 | semidirect |
| 3. #30656631 | C2 | semidirect |
| 4. #30656618 | C2 | semidirect |
| 6. C4×#16861597 | C2 | semidirect |
| 7. C22⋊C4×Dic257 | C2 | semidirect |
| 8. C22⋊C4×Dic257 | C2 | semidirect |
| 12. #22551573 | C4 | semidirect |
| 36. C22×Dic257 | C2×C4 | semidirect |
| 42. #16861597 | C2×C4 | semidirect |
| 46. C22⋊Dic257 | C2×C4 | semidirect |
| 126. C257 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551573 | 2 |
| #30656631 | 2 |
| #30656618 | 2 |
| #30656617 | 2 |
| C4×#16861597 | 2 |
| C22⋊C4×Dic257 | 2 |
| #390×C257 | 2 |
| #2374 | 257 |