Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 46. C3×M32 | Q8 | semidirect |
| 54. #819 | Q8 | semidirect |
| 61. C2×C3⋊C16 | Q8 | semidirect |
| 129. M32 | Dic6 | semidirect |
| 261. C3 | #13456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79173 | 2 |
| C3×#2159 | 2 |
| #70625 | 2 |
| C2×#4490 | 2 |
| #67817 | 2 |
| #67815 | 2 |
| #67724 | 2 |
| #13456 | 3 |