Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 138 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. #16811493 | C2 | semidirect |
| 8. D53⋊M16 | C4 | semidirect |
| 13. C2×C4×#6157 | C4 | semidirect |
| 16. #13133176 | C4 | semidirect |
| 20. C4⋊C4×D53 | C4 | semidirect |
| 23. #117×C53 | C4 | semidirect |
| 43. C4×#6157 | C2×C4 | semidirect |
| 45. #11719936 | C2×C4 | semidirect |
| 47. C4⋊C4×C53 | C2×C4 | semidirect |
| 52. C4⋊Dic53 | C2×C4 | semidirect |
| 112. D53 | #339 | semidirect |
| 117. C53 | C2×#339 | semidirect |
| 129. #117 | #6157 | semidirect |
| 159. C4⋊C4 | C2×#6157 | semidirect |