Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 4. #16810440 | C2 | semidirect |
| 5. #16810439 | C2 | semidirect |
| 6. #16810438 | C2 | semidirect |
| 7. C53×#362 | C2 | semidirect |
| 89. D53 | #362 | direct (N × H) |
| 96. #362 | D53 | direct (N × H) |
| 97. C53 | C2×#362 | semidirect |