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. #89471 | C2 | semidirect |
| 4. C7×#335 | C2 | semidirect |
| 5. #89281 | C2 | semidirect |
| 36. #335 | D7 | semidirect |
| 45. D28 | Q16 | semidirect |
| 111. C7 | #1669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89618 | 2 |
| #89471 | 2 |
| C8×D28 | 2 |
| C7×#335 | 2 |
| #89281 | 2 |
| #1669 | 7 |