Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
156 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 156 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 |
|---|---|---|
| 52. C7×Q8 | Q16 | semidirect |
| 118. Q8 | #1144 | semidirect |
| 131. C7 | #1670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#475 | 2 |
| #89864 | 2 |
| Q8×C7⋊C8 | 2 |
| #89792 | 2 |
| #89342 | 2 |
| #89281 | 2 |
| #89274 | 2 |
| #1670 | 7 |