Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1734 conjugacy classes of subgroups; only the 1035 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 1035 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. C4×#803 | C2 | semidirect |
| 4. C42×C3⋊C8 | C2 | semidirect |
| 12. C4×#208 | C4 | direct (N × H) |
| 30. #803 | C2×C4 | semidirect |
| 31. C4×C3⋊C8 | C2×C4 | semidirect |
| 51. C3×C42 | M16 | semidirect |
| 54. #208 | C42 | direct (N × H) |
| 80. C3⋊C8 | C2×C42 | semidirect |
| 92. C42 | #208 | direct (N × H) |
| 102. C3×C4 | C4×M16 | semidirect |
| 124. C4 | C4×#208 | direct (N × H) |
| 127. C3 | C42×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C43 | 2 |
| C2×C4×#208 | 2 |
| C4×#803 | 2 |
| C42×C3⋊C8 | 2 |
| C42×M16 | 3 |