Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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. #16810661 | C2 | semidirect |
| 3. #16810425 | C2 | semidirect |
| 4. C2×M32×C53 | C2 | semidirect |
| 8. C2×D424 | C4 | semidirect |
| 11. #13133151 | C22 | semidirect |
| 15. C2×C16×C53 | C22 | semidirect |
| 64. C2×M32 | D53 | semidirect |
| 67. C53 | #2140 | semidirect |
| 76. C2×C16 | C2×D53 | semidirect |