Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 3. #70753 | C2 | semidirect |
| 4. #70516 | C2 | semidirect |
| 6. C3×#1299 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 35. #1299 | D3 | semidirect |
| 327. C3 | #8901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79052 | 2 |
| #70754 | 2 |
| #70753 | 2 |
| #70516 | 2 |
| #69854 | 2 |
| C3×#1299 | 2 |
| #67667 | 2 |
| #8901 | 3 |