Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 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. #89847 | C2 | semidirect |
| 3. C8×Dic14 | C2 | semidirect |
| 4. #89339 | C2 | semidirect |
| 5. #89253 | C2 | semidirect |
| 50. Dic14 | D8 | semidirect |
| 52. C7×C8 | SD16 | semidirect |
| 112. C8 | #1142 | semidirect |
| 113. C7 | #1668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#493 | 2 |
| #89847 | 2 |
| C8×Dic14 | 2 |
| #89339 | 2 |
| #89253 | 2 |
| #1668 | 7 |