Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
166 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 166 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. #89953 | C2 | semidirect |
| 5. #89359 | C2 | semidirect |
| 6. #89298 | C2 | semidirect |
| 7. Dic7⋊C16 | C2 | semidirect |
| 89. Dic7 | SD32 | semidirect |
| 131. C7 | #2208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD32 | 2 |
| #89953 | 2 |
| D8×Dic7 | 2 |
| C2×#6401 | 2 |
| #89359 | 2 |
| #89298 | 2 |
| Dic7⋊C16 | 2 |
| #2208 | 7 |