Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 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. #72084 | C2 | semidirect |
| 3. C2×#4567 | C2 | semidirect |
| 4. C2×#4506 | C2 | semidirect |
| 5. C2×#4502 | C2 | semidirect |
| 10. C2×C3×Q32 | C4 | semidirect |
| 11. C2×C3×SD32 | C4 | semidirect |
| 12. C2×C3×D16 | C4 | semidirect |
| 58. C2×Q32 | Dic3 | semidirect |
| 59. C2×SD32 | Dic3 | semidirect |
| 60. C2×D16 | Dic3 | semidirect |
| 243. C3 | #13242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#508 | 2 |
| #72084 | 2 |
| C2×#4567 | 2 |
| C2×#4506 | 2 |
| C2×#4502 | 2 |
| #13242 | 3 |