Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. #70837 | C2 | semidirect |
| 5. #69566 | C2 | semidirect |
| 6. C3×#1288 | C2 | semidirect |
| 7. #67666 | C2 | semidirect |
| 18. #4694 | C4 | semidirect |
| 19. #4694 | C4 | semidirect |
| 32. #1288 | D3 | semidirect |
| 50. #869 | C2×C4 | semidirect |
| 51. #869 | C2×C4 | semidirect |
| 58. C3×C4×C8 | C2×C4 | semidirect |
| 159. C4×C8 | C4×D3 | semidirect |
| 329. C3 | #9425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78526 | 2 |
| #74298 | 2 |
| #70837 | 2 |
| #70818 | 2 |
| #69566 | 2 |
| C3×#1288 | 2 |
| #67666 | 2 |
| #9425 | 3 |