Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #16810449 | C2 | semidirect |
| 4. #16810448 | C2 | semidirect |
| 5. C53×#366 | C2 | semidirect |
| 9. C16×D53 | C4 | semidirect |
| 23. C16×C53 | C2×C4 | semidirect |
| 24. #11719908 | C2×C4 | semidirect |
| 49. D53 | #366 | direct (N × H) |
| 54. #366 | D53 | direct (N × H) |
| 55. C53 | C2×#366 | semidirect |
| 74. C16 | C4×D53 | semidirect |