Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #16811421 | C2 | semidirect |
| 2. C2×#13133243 | C2 | semidirect |
| 3. #16811389 | C2 | semidirect |
| 4. #16810890 | C2 | semidirect |
| 5. #16810883 | C2 | semidirect |
| 6. #16810672 | C2 | semidirect |
| 7. #16810607 | C2 | semidirect |
| 8. C2×#13133134 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 11. #13133248 | C22 | semidirect |
| 15. #13133243 | C22 | semidirect |
| 21. #13133223 | C22 | semidirect |
| 26. #13133153 | C22 | semidirect |
| 27. #13133136 | C22 | semidirect |
| 28. #13133134 | C22 | semidirect |
| 29. #13133134 | C22 | semidirect |
| 34. C2×SD16×C53 | C22 | semidirect |
| 35. C2×D8×C53 | C22 | semidirect |
| 150. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 157. C53 | #3068 | semidirect |
| 171. C2×SD16 | C2×D53 | semidirect |
| 173. C2×D8 | C2×D53 | semidirect |