Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 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. #16811549 | C2 | direct (N × H) |
| 8. C2×#11719908 | C4 | semidirect |
| 9. C16×D53 | C4 | semidirect |
| 11. C2×C16×C53 | C4 | semidirect |
| 22. C16×C53 | C2×C4 | semidirect |
| 23. #11719908 | C2×C4 | semidirect |
| 48. C2×C53 | #366 | semidirect |
| 50. D53 | #366 | semidirect |
| 56. C53 | C2×#366 | semidirect |
| 62. C2×C16 | #6157 | semidirect |
| 76. C16 | C2×#6157 | semidirect |
| 103. C2 | #16811549 | direct (N × H) |