Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
538 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 121 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×#5152 | C2 | semidirect |
| 3. #72085 | C2 | semidirect |
| 4. C2×#4566 | C2 | semidirect |
| 5. C2×#4563 | C2 | semidirect |
| 6. #67816 | C2 | semidirect |
| 7. #67811 | C2 | semidirect |
| 14. C2×C3×SD32 | C4 | semidirect |
| 15. C2×C3×D16 | C4 | semidirect |
| 42. C2×C3×Q16 | C2×C4 | semidirect |
| 48. C2×C3×D8 | C2×C4 | semidirect |
| 63. C2×C3×C16 | C2×C4 | semidirect |
| 81. C2×SD32 | Dic3 | semidirect |
| 82. C2×D16 | Dic3 | semidirect |
| 151. C2×Q16 | C2×Dic3 | semidirect |
| 157. C2×D8 | C2×Dic3 | semidirect |
| 175. C2×C16 | C2×Dic3 | semidirect |
| 350. C3 | #13037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#509 | 2 |
| C2×#5152 | 2 |
| #72085 | 2 |
| C2×#4566 | 2 |
| C2×#4563 | 2 |
| #67816 | 2 |
| #67811 | 2 |
| #13037 | 3 |