Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 3. C22×Dic28 | C2 | semidirect |
| 5. #89746 | C2 | semidirect |
| 6. C2×#6384 | C2 | semidirect |
| 7. #89345 | C2 | semidirect |
| 226. C7 | #2015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6499 | 2 |
| C22×#1142 | 2 |
| C22×Dic28 | 2 |
| C2×C7×#102 | 2 |
| #89746 | 2 |
| C2×#6384 | 2 |
| #89345 | 2 |
| #2015 | 7 |