Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 4. #89894 | C2 | semidirect |
| 5. C2×#6377 | C2 | semidirect |
| 6. #89353 | C2 | semidirect |
| 7. #89318 | C2 | semidirect |
| 12. #6511 | C4 | semidirect |
| 19. C7×#104 | C4 | semidirect |
| 20. #6409 | C4 | semidirect |
| 21. #6406 | C4 | semidirect |
| 99. #104 | Dic7 | semidirect |
| 178. C7 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6511 | 2 |
| C2×C7×#104 | 2 |
| #90005 | 2 |
| #89894 | 2 |
| C2×#6377 | 2 |
| #89353 | 2 |
| #89318 | 2 |
| #1765 | 7 |