Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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×#6403 | C2 | semidirect |
| 3. C2×#6401 | C2 | semidirect |
| 4. #89888 | C2 | semidirect |
| 5. #89359 | C2 | semidirect |
| 6. #89357 | C2 | semidirect |
| 7. C22⋊(C7⋊C16) | C2 | 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×C7×#135 | 2 |
| C2×#6403 | 2 |
| C2×#6401 | 2 |
| #89888 | 2 |
| #89359 | 2 |
| #89357 | 2 |
| C22⋊(C7⋊C16) | 2 |
| #2189 | 7 |