Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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. #70771 | C2 | semidirect |
| 4. #69801 | C2 | semidirect |
| 6. C3×#1275 | C2 | semidirect |
| 7. #67747 | C2 | semidirect |
| 36. #1275 | D3 | semidirect |
| 329. C3 | #9285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79306 | 2 |
| #79290 | 2 |
| #70771 | 2 |
| #69801 | 2 |
| #69798 | 2 |
| C3×#1275 | 2 |
| #67747 | 2 |
| #9285 | 3 |