Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #16811638 | C2 | semidirect |
| 4. M16×#6157 | C2 | semidirect |
| 5. #16811506 | C2 | semidirect |
| 6. #16811495 | C2 | semidirect |
| 23. #13133136 | C4 | semidirect |
| 24. #13133133 | C4 | semidirect |
| 25. #13133133 | C4 | semidirect |
| 26. #101×C53 | C4 | semidirect |
| 113. C53 | #1932 | semidirect |
| 128. #101 | #6157 | semidirect |