Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #89892 | C2 | semidirect |
| 5. #89352 | C2 | semidirect |
| 11. #6507 | C4 | semidirect |
| 12. #6499 | C4 | semidirect |
| 144. C7 | #1909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#568 | 2 |
| #90516 | 2 |
| #90012 | 2 |
| #89892 | 2 |
| #89352 | 2 |
| #1909 | 7 |