Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 158 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 |
|---|---|---|
| 26. C3×C32 | Q8 | semidirect |
| 27. C3⋊C32 | Q8 | semidirect |
| 53. C32 | Dic6 | semidirect |
| 99. C3 | #13731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69320 | 2 |
| C3×#1423 | 2 |
| #67591 | 2 |
| Dic3×C32 | 2 |
| #67575 | 2 |
| #13731 | 3 |