Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
186 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 27 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 |
|---|---|---|
| 2. #67792 | C2 | semidirect |
| 5. C3×#493 | C4 | semidirect |
| 7. C3×C82 | C4 | semidirect |
| 20. #493 | Dic3 | semidirect |
| 23. C82 | Dic3 | semidirect |
| 96. C3 | #7529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1712 | 2 |
| #67792 | 2 |
| #7529 | 3 |