Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2018 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 2018 conjugacy classes of subgroups — too many to draw. Only its 987 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 |
|---|---|---|
| 7. C2×C3×C4×Q8 | C4 | semidirect |
| 10. #5812 | C4 | semidirect |
| 39. C2×C4×Q8 | Dic3 | semidirect |
| 164. C3 | #20355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#519 | 2 |
| C2×#5812 | 2 |
| #71592 | 2 |
| #20355 | 3 |