Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×C7×M32 | C2 | semidirect |
| 3. #89878 | C2 | semidirect |
| 4. #89304 | C2 | semidirect |
| 10. C2×D56 | C4 | semidirect |
| 13. C2×C7×C16 | C22 | semidirect |
| 14. #6392 | C22 | semidirect |
| 35. C2×M32 | D7 | semidirect |
| 61. C2×C16 | C2×D7 | semidirect |
| 110. C7 | #2140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D56 | 2 |
| C2×C7×M32 | 2 |
| #89878 | 2 |
| #89304 | 2 |
| #2140 | 7 |