Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 125 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. #90233 | C2 | semidirect |
| 3. C7×C8×D4 | C2 | semidirect |
| 4. #89886 | C2 | semidirect |
| 5. #89878 | C2 | semidirect |
| 6. #89622 | C2 | semidirect |
| 7. #89618 | C2 | semidirect |
| 8. #89509 | C2 | semidirect |
| 9. #89495 | C2 | semidirect |
| 10. C4×#1132 | C2 | semidirect |
| 11. #89452 | C2 | semidirect |
| 83. C8×D4 | D7 | semidirect |
| 218. C7 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90254 | 2 |
| #90233 | 2 |
| C7×C8×D4 | 2 |
| #89886 | 2 |
| #89878 | 2 |
| #89622 | 2 |
| #89618 | 2 |
| #89509 | 2 |
| #89495 | 2 |
| C4×#1132 | 2 |
| #89452 | 2 |
| #3340 | 7 |