Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
518 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#4851 | C2 | semidirect |
| 4. #70786 | C2 | semidirect |
| 5. #70507 | C2 | semidirect |
| 7. C3×#1301 | C2 | semidirect |
| 38. #1301 | D3 | semidirect |
| 390. C3 | #10189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79269 | 2 |
| #79067 | 2 |
| C2×#4851 | 2 |
| #70786 | 2 |
| #70507 | 2 |
| #70426 | 2 |
| C3×#1301 | 2 |
| #10189 | 3 |