Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
392 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 145 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. #16810388 | C2 | semidirect |
| 4. #16810387 | C2 | semidirect |
| 5. C53×#341 | C2 | semidirect |
| 81. D53 | #341 | direct (N × H) |
| 86. #341 | D53 | direct (N × H) |
| 87. C53 | C2×#341 | semidirect |