Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16810973 | C2 | semidirect |
| 3. #16810951 | C2 | semidirect |
| 4. #16810908 | C2 | semidirect |
| 5. #16810854 | C2 | semidirect |
| 6. #16810825 | C2 | semidirect |
| 7. #16810762 | C2 | semidirect |
| 8. C4×#11719924 | C2 | semidirect |
| 9. D4×#88322 | C2 | semidirect |
| 10. C2×#13133141 | C2 | semidirect |
| 11. D4×Q8×C53 | C2 | semidirect |
| 83. Q8×C53 | #41 | semidirect |
| 84. D4×C53 | SD16 | semidirect |
| 129. D4×Q8 | D53 | semidirect |
| 140. C53 | #3298 | semidirect |
| 213. Q8 | #11719947 | semidirect |
| 217. D4 | #11719924 | semidirect |