Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 4. #89453 | C2 | semidirect |
| 5. #89281 | C2 | semidirect |
| 6. #89277 | C2 | semidirect |
| 7. #89252 | C2 | semidirect |
| 138. C7 | #1679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×D4 | 2 |
| #89791 | 2 |
| #89779 | 2 |
| #89453 | 2 |
| #89281 | 2 |
| #89277 | 2 |
| #89252 | 2 |
| #1679 | 7 |