Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #16811245 | C2 | semidirect |
| 2. #16811027 | C2 | semidirect |
| 3. #16811008 | C2 | semidirect |
| 4. #16810984 | C2 | semidirect |
| 5. #16810872 | C2 | semidirect |
| 6. #16810861 | C2 | semidirect |
| 8. #16810721 | C2 | semidirect |
| 9. C4×D424 | C2 | semidirect |
| 10. #16810577 | C2 | semidirect |
| 11. C4×Q16×C53 | C2 | semidirect |
| 126. C4×Q16 | D53 | semidirect |
| 129. C53 | #3175 | semidirect |