Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
450 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 123 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×#1450 | C2 | semidirect |
| 3. #70780 | C2 | semidirect |
| 4. #70779 | C2 | semidirect |
| 7. #69791 | C2 | semidirect |
| 33. #1450 | D3 | semidirect |
| 291. C3 | #9769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4694 | 2 |
| C3×#1450 | 2 |
| #70780 | 2 |
| #70779 | 2 |
| #70774 | 2 |
| #69791 | 2 |
| #9769 | 3 |