Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
404 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 50. #836 | Q8 | semidirect |
| 269. C3 | #13301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2568 | 2 |
| #71637 | 2 |
| C4×#836 | 2 |
| #67644 | 2 |
| #13301 | 3 |