Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #90191 | C2 | semidirect |
| 4. C7×#343 | C2 | semidirect |
| 5. #89350 | C2 | semidirect |
| 25. C2×D28 | Q8 | semidirect |
| 42. #343 | D7 | semidirect |
| 140. C7 | #2027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90191 | 2 |
| #89903 | 2 |
| #89760 | 2 |
| C7×#343 | 2 |
| #89350 | 2 |
| #2027 | 7 |