Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 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×#13133223 | C2 | semidirect |
| 3. #16810895 | C2 | semidirect |
| 4. #16810890 | C2 | semidirect |
| 5. #16810883 | C2 | semidirect |
| 6. C2×#13133153 | C2 | semidirect |
| 7. #16810607 | C2 | semidirect |
| 8. C2×#135×C53 | C2 | semidirect |
| 23. #13133153 | C22 | semidirect |
| 24. #13133153 | C22 | semidirect |
| 25. #13133136 | C22 | semidirect |
| 26. #13133134 | C22 | semidirect |
| 32. C2×Q16×C53 | C22 | semidirect |
| 33. C2×SD16×C53 | C22 | semidirect |
| 34. C2×D8×C53 | C22 | semidirect |
| 134. C2×#135 | D53 | semidirect |
| 141. C53 | #3067 | semidirect |
| 153. C2×Q16 | C2×D53 | semidirect |
| 154. C2×SD16 | C2×D53 | semidirect |
| 155. C2×D8 | C2×D53 | semidirect |