Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
384 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 2. C3×#1568 | C2 | semidirect |
| 3. #70831 | C2 | semidirect |
| 5. #70812 | C2 | semidirect |
| 7. #69725 | C2 | semidirect |
| 33. #1568 | D3 | semidirect |
| 343. C3 | #9790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4697 | 2 |
| C3×#1568 | 2 |
| #70831 | 2 |
| #70828 | 2 |
| #70812 | 2 |
| #70804 | 2 |
| #69725 | 2 |
| #9790 | 3 |