Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
174 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 174 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. D8×#6157 | C2 | semidirect |
| 2. #16811549 | C2 | semidirect |
| 3. #16811535 | C2 | semidirect |
| 4. C16×#6157 | C2 | semidirect |
| 12. D848 | C4 | semidirect |
| 13. #13133158 | C4 | semidirect |
| 15. D16×C53 | C4 | semidirect |
| 22. D8×C53 | C2×C4 | semidirect |
| 24. D424 | C2×C4 | semidirect |
| 27. C16×C53 | C2×C4 | semidirect |
| 28. #11719908 | C2×C4 | semidirect |
| 48. #6157 | D16 | direct (N × H) |
| 62. C53 | C4×D16 | semidirect |
| 67. D16 | #6157 | direct (N × H) |
| 77. D8 | C2×#6157 | semidirect |
| 85. C16 | C2×#6157 | semidirect |