Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#13133240 | C2 | semidirect |
| 2. C2×Q16×D53 | C2 | semidirect |
| 3. #16811285 | C2 | semidirect |
| 4. #16811007 | C2 | semidirect |
| 5. #16810865 | C2 | semidirect |
| 6. #16810860 | C2 | semidirect |
| 7. #16810845 | C2 | semidirect |
| 8. #16810788 | C2 | semidirect |
| 9. #16810763 | C2 | semidirect |
| 10. C8×D212 | C2 | semidirect |
| 11. C4×Q16×C53 | C2 | semidirect |
| 56. Q16×C53 | D4 | semidirect |
| 120. C2×D53 | #135 | semidirect |
| 146. C4×Q16 | D53 | semidirect |
| 148. C53 | #3285 | semidirect |
| 195. Q16 | D212 | semidirect |