Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 104. Dic3 | Q64 | semidirect |
| 124. C3 | #13726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q64 | 2 |
| #71499 | 2 |
| C2×#4522 | 2 |
| C2×Dic48 | 2 |
| Dic3×C32 | 2 |
| #13726 | 3 |