Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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. #16811630 | C2 | semidirect |
| 4. C2×C8×#6157 | C2 | semidirect |
| 5. #16811499 | C2 | semidirect |
| 6. #16811493 | C2 | semidirect |
| 21. #13133142 | C4 | semidirect |
| 22. #13133140 | C4 | semidirect |
| 23. #13133138 | C4 | semidirect |
| 24. #102×C53 | C4 | semidirect |
| 113. C53 | #1937 | semidirect |
| 127. #102 | #6157 | semidirect |