Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
198 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 81 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. #89342 | C2 | semidirect |
| 5. #89341 | C2 | semidirect |
| 128. C7 | #1554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#533 | 2 |
| #89698 | 2 |
| #89697 | 2 |
| #89342 | 2 |
| #89341 | 2 |
| #1554 | 7 |