Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
316 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 45. C3×M32 | Q8 | semidirect |
| 59. #812 | Q8 | semidirect |
| 129. M32 | Dic6 | semidirect |
| 244. C3 | #13270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78445 | 2 |
| #71425 | 2 |
| #71423 | 2 |
| C3×#1376 | 2 |
| #67814 | 2 |
| #67813 | 2 |
| #67658 | 2 |
| #13270 | 3 |