Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 43. C3×M32 | Q8 | semidirect |
| 49. #818 | Q8 | semidirect |
| 57. #812 | Q8 | semidirect |
| 119. M32 | Dic6 | semidirect |
| 234. C3 | #13457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4855 | 2 |
| C2×C3×#365 | 2 |
| #70704 | 2 |
| C2×#4494 | 2 |
| #67819 | 2 |
| #67810 | 2 |
| #67721 | 2 |
| #13457 | 3 |