Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
230 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #16810650 | C2 | semidirect |
| 4. C2×C8×Dic53 | C2 | semidirect |
| 5. #16810388 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 19. #103×C53 | C4 | semidirect |
| 20. #102×C53 | C4 | semidirect |
| 98. C53 | #1937 | semidirect |
| 108. #103 | Dic53 | semidirect |
| 109. #102 | Dic53 | semidirect |