Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811333 | C2 | semidirect |
| 3. #16811021 | C2 | semidirect |
| 4. #16810952 | C2 | semidirect |
| 5. #16810940 | C2 | semidirect |
| 6. #16810913 | C2 | semidirect |
| 7. #16810908 | C2 | semidirect |
| 8. #16810849 | C2 | semidirect |
| 9. C8×D212 | C2 | semidirect |
| 10. #106×D53 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 91. D212 | SD16 | semidirect |
| 99. C8×C53 | #41 | semidirect |
| 132. C4×SD16 | D53 | semidirect |
| 135. C53 | #3335 | semidirect |
| 224. C8 | #11719945 | semidirect |