Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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. #89864 | C2 | semidirect |
| 3. #89850 | C2 | semidirect |
| 6. #89454 | C2 | semidirect |
| 7. #89249 | C2 | semidirect |
| 124. C7 | #1722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#486 | 2 |
| #89864 | 2 |
| #89850 | 2 |
| #89848 | 2 |
| #89842 | 2 |
| #89454 | 2 |
| #89249 | 2 |
| #1722 | 7 |