Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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. #89850 | C2 | semidirect |
| 5. #89342 | C2 | semidirect |
| 6. #89277 | C2 | semidirect |
| 7. #89275 | C2 | semidirect |
| 69. C7⋊C8 | SD16 | semidirect |
| 140. C7 | #1693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#461 | 2 |
| #89850 | 2 |
| #89791 | 2 |
| #89784 | 2 |
| #89342 | 2 |
| #89277 | 2 |
| #89275 | 2 |
| #1693 | 7 |