Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
144 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 67 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. #16810453 | C2 | semidirect |
| 4. #16810452 | C2 | semidirect |
| 5. C53×#368 | C2 | semidirect |
| 53. D53 | #368 | direct (N × H) |
| 58. #368 | D53 | direct (N × H) |
| 59. C53 | C2×#368 | semidirect |