Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16811356 | C2 | semidirect |
| 2. #16811007 | C2 | semidirect |
| 3. #16811006 | C2 | semidirect |
| 5. #16810838 | C2 | semidirect |
| 6. #16810837 | C2 | semidirect |
| 7. #16810822 | C2 | semidirect |
| 8. C8×Dic106 | C2 | semidirect |
| 9. #16810717 | C2 | semidirect |
| 10. #16810705 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 131. C4×D8 | D53 | semidirect |
| 132. C53 | #3396 | semidirect |