Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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. #89866 | C2 | semidirect |
| 4. C8×Dic14 | C2 | semidirect |
| 5. #89342 | C2 | semidirect |
| 7. #89252 | C2 | semidirect |
| 65. Dic14 | SD16 | semidirect |
| 67. C7×C8 | SD16 | semidirect |
| 141. C8 | #1142 | semidirect |
| 142. C7 | #1666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#492 | 2 |
| #89866 | 2 |
| #89847 | 2 |
| C8×Dic14 | 2 |
| #89342 | 2 |
| #89339 | 2 |
| #89252 | 2 |
| #1666 | 7 |