Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 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. C2×#6391 | C2 | semidirect |
| 5. C2×#6390 | C2 | semidirect |
| 6. C2×#6390 | C2 | semidirect |
| 7. #89346 | C2 | semidirect |
| 227. C7 | #2035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6487 | 2 |
| C2×C7×C22⋊C8 | 2 |
| #89984 | 2 |
| C2×#6391 | 2 |
| C2×#6390 | 2 |
| #89346 | 2 |
| #2035 | 7 |