Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
310 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
| 62. C2×C3⋊C16 | Q8 | semidirect |
| 129. M32 | Dic6 | semidirect |
| 246. C3 | #13460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79110 | 2 |
| C2×C3×#365 | 2 |
| #70706 | 2 |
| #70685 | 2 |
| #67822 | 2 |
| #67814 | 2 |
| #67720 | 2 |
| #13460 | 3 |