Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 4. #16810384 | C2 | semidirect |
| 5. #16810383 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 7. C53×#339 | C2 | semidirect |
| 12. M16×D53 | C4 | semidirect |
| 15. #13133175 | C4 | semidirect |
| 18. #13133174 | C4 | semidirect |
| 21. C4⋊C4×D53 | C4 | semidirect |
| 44. M16×C53 | C2×C4 | semidirect |
| 50. C42×C53 | C2×C4 | semidirect |
| 60. C4×Dic53 | C2×C4 | semidirect |
| 62. #11719917 | C2×C4 | semidirect |
| 132. #339 | D53 | semidirect |
| 133. C53 | #1733 | semidirect |
| 173. M16 | C4×D53 | semidirect |
| 191. C42 | C4×D53 | semidirect |