Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
752 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 3. #16811616 | C2 | direct (N × H) |
| 4. C2×#13133280 | C2 | semidirect |
| 16. #13133280 | C22 | semidirect |
| 18. C22×Dic106 | C4 | semidirect |
| 23. C2×Q8×D53 | C4 | semidirect |
| 24. C2×Q8×D53 | C4 | semidirect |
| 29. C22×Q8×C53 | C4 | semidirect |
| 35. C2×Q8×C53 | C2×C4 | semidirect |
| 48. Q8×D53 | C2×C4 | semidirect |
| 69. C2×Dic106 | C2×C4 | semidirect |
| 143. C2×C53 | #419 | semidirect |
| 146. D53 | #419 | semidirect |
| 153. C53 | C2×#419 | semidirect |
| 164. C22×Q8 | #6157 | semidirect |
| 200. C2×Q8 | C2×#6157 | semidirect |
| 293. C2 | #16811616 | direct (N × H) |