Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
274 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 274 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. #89707 | C2 | semidirect |
| 4. #89324 | C2 | semidirect |
| 5. #89319 | C2 | semidirect |
| 156. C7 | #2071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#390 | 2 |
| C2×#6406 | 2 |
| #89707 | 2 |
| #89324 | 2 |
| #89319 | 2 |
| #2071 | 7 |