Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 36. #1144 | Q8 | direct (N × H) |
| 52. C7×Q8 | Q16 | semidirect |
| 117. Q8 | #1144 | direct (N × H) |
| 128. C7 | Q8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q82 | 2 |
| Q8×Dic14 | 2 |
| #89863 | 2 |
| #89850 | 2 |
| C4×#1144 | 2 |
| Q8×C7⋊C8 | 2 |
| #89793 | 2 |
| Q8×Q16 | 7 |