Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #16811669 | C2 | semidirect |
| 2. #16811664 | C2 | semidirect |
| 3. #16811547 | C2 | semidirect |
| 4. #16811541 | C2 | semidirect |
| 5. #16811540 | C2 | semidirect |
| 6. #16811514 | C2 | semidirect |
| 18. #13133160 | C4 | semidirect |
| 19. D848 | C4 | semidirect |
| 20. #13133158 | C4 | semidirect |
| 22. SD32×C53 | C4 | semidirect |
| 33. Q16×C53 | C2×C4 | semidirect |
| 38. D424 | C2×C4 | semidirect |
| 41. C16×C53 | C2×C4 | semidirect |
| 42. #11719908 | C2×C4 | semidirect |
| 83. C53 | AGL(1,ℤ/16) | semidirect |
| 89. SD32 | #6157 | semidirect |
| 102. Q16 | C2×#6157 | semidirect |
| 118. C16 | C2×#6157 | semidirect |