Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
178 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 178 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 |
|---|---|---|
| 1. C2×Dic56 | C2 | semidirect |
| 3. #89471 | C2 | semidirect |
| 5. C7×#346 | C2 | semidirect |
| 37. #346 | D7 | semidirect |
| 101. C7 | #2251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic56 | 2 |
| C2×#6374 | 2 |
| #89471 | 2 |
| #89468 | 2 |
| C7×#346 | 2 |
| #2251 | 7 |