Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
136 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 51 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. #89455 | C2 | semidirect |
| 3. C7×C4⋊C16 | C2 | semidirect |
| 6. #89300 | C2 | semidirect |
| 7. #89299 | C2 | semidirect |
| 39. C4⋊C16 | D7 | semidirect |
| 109. C7 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D56 | 2 |
| #89455 | 2 |
| C7×C4⋊C16 | 2 |
| #89304 | 2 |
| #89300 | 2 |
| #89299 | 2 |
| #2228 | 7 |