Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×C3×#359 | C2 | semidirect |
| 3. #72084 | C2 | semidirect |
| 4. C2×#4510 | C2 | semidirect |
| 5. C2×#4502 | C2 | semidirect |
| 6. #70696 | C2 | semidirect |
| 7. C2×#4493 | C2 | semidirect |
| 17. C2×#829 | C4 | semidirect |
| 18. C2×#828 | C4 | semidirect |
| 19. C2×#827 | C4 | semidirect |
| 20. C2×#826 | C4 | semidirect |
| 33. C2×#359 | D3 | semidirect |
| 350. C3 | #13242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5194 | 2 |
| C2×C3×#359 | 2 |
| #72084 | 2 |
| C2×#4510 | 2 |
| C2×#4502 | 2 |
| #70696 | 2 |
| C2×#4493 | 2 |
| #13242 | 3 |