Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
558 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 558 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×#1452 | C2 | semidirect |
| 3. #70774 | C2 | semidirect |
| 4. #69791 | C2 | semidirect |
| 19. #1452 | D3 | semidirect |
| 156. C3 | #9780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4695 | 2 |
| C3×#1452 | 2 |
| #70774 | 2 |
| #69791 | 2 |
| #9780 | 3 |