Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 1. Q16×#6157 | C2 | semidirect |
| 3. #16811550 | C2 | semidirect |
| 4. #16811536 | C2 | semidirect |
| 6. C16×#6157 | C2 | semidirect |
| 18. #13133162 | C4 | semidirect |
| 19. #13133161 | C4 | semidirect |
| 20. #13133160 | C4 | semidirect |
| 22. SD32×C53 | C4 | semidirect |
| 33. Q16×C53 | C2×C4 | semidirect |
| 37. Dic212 | C2×C4 | semidirect |
| 41. C16×C53 | C2×C4 | semidirect |
| 42. #11719908 | C2×C4 | semidirect |
| 68. #6157 | SD32 | direct (N × H) |
| 86. C53 | C4×SD32 | semidirect |
| 94. SD32 | #6157 | direct (N × H) |
| 107. Q16 | C2×#6157 | semidirect |
| 121. C16 | C2×#6157 | semidirect |