Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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. #90291 | C2 | semidirect |
| 3. #89925 | C2 | semidirect |
| 4. #89909 | C2 | semidirect |
| 5. #89890 | C2 | semidirect |
| 6. #89814 | C2 | semidirect |
| 7. #89629 | C2 | semidirect |
| 8. #89539 | C2 | semidirect |
| 9. #89535 | C2 | semidirect |
| 188. C7 | #3256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90291 | 2 |
| C7×#469 | 2 |
| #89925 | 2 |
| #89909 | 2 |
| #89890 | 2 |
| #89814 | 2 |
| #89629 | 2 |
| #89539 | 2 |
| #89535 | 2 |
| #3256 | 7 |