Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #89888 | C2 | semidirect |
| 3. C2×Dic56 | C2 | semidirect |
| 4. C2×#6374 | C2 | semidirect |
| 5. C7×C22⋊C16 | C2 | semidirect |
| 6. #89304 | C2 | semidirect |
| 7. #89298 | C2 | semidirect |
| 54. C22⋊C16 | D7 | semidirect |
| 152. C7 | #2189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6467 | 2 |
| #89888 | 2 |
| C2×Dic56 | 2 |
| C2×#6374 | 2 |
| C7×C22⋊C16 | 2 |
| #89304 | 2 |
| #89298 | 2 |
| #2189 | 7 |