Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
414 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2155 | C2 | semidirect |
| 3. #71425 | C2 | semidirect |
| 4. #70709 | C2 | semidirect |
| 5. #70690 | C2 | semidirect |
| 6. #70658 | C2 | semidirect |
| 7. #70652 | C2 | semidirect |
| 22. C2×#800 | C4 | semidirect |
| 23. C2×D48 | C4 | semidirect |
| 29. #2155 | D3 | semidirect |
| 328. C3 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4908 | 2 |
| C3×#2155 | 2 |
| #71425 | 2 |
| #70709 | 2 |
| #70690 | 2 |
| #70658 | 2 |
| #70652 | 2 |
| #13247 | 3 |