Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
144 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 47 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×#6401 | C2 | semidirect |
| 3. #89915 | C2 | semidirect |
| 4. #89912 | C2 | semidirect |
| 5. #89358 | C2 | semidirect |
| 6. #89291 | C2 | semidirect |
| 7. #89288 | C2 | semidirect |
| 130. C7 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#472 | 2 |
| C2×#6401 | 2 |
| #89915 | 2 |
| #89912 | 2 |
| #89358 | 2 |
| #89291 | 2 |
| #89288 | 2 |
| #2223 | 7 |