Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
376 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 113 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. #89993 | C2 | semidirect |
| 3. C2×#6406 | C2 | semidirect |
| 4. C2×#6391 | C2 | semidirect |
| 5. C2×#6389 | C2 | semidirect |
| 9. C2×C7×D8 | C4 | semidirect |
| 66. C7×C8 | C22⋊C4 | semidirect |
| 71. C2×D8 | Dic7 | semidirect |
| 143. C8 | C22⋊Dic7 | semidirect |
| 144. C7 | #1972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D8 | 2 |
| #89993 | 2 |
| C2×#6406 | 2 |
| C2×#6391 | 2 |
| C2×#6389 | 2 |
| #1972 | 7 |