Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 204 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 |
|---|---|---|
| 4. #89897 | C2 | semidirect |
| 5. #89351 | C2 | semidirect |
| 6. #89328 | C2 | semidirect |
| 7. #89326 | C2 | semidirect |
| 151. C7 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#418 | 2 |
| C2×#6407 | 2 |
| #89987 | 2 |
| #89897 | 2 |
| #89351 | 2 |
| #89328 | 2 |
| #89326 | 2 |
| #2081 | 7 |