Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×#13133182 | C2 | semidirect |
| 4. #16810722 | C2 | direct (N × H) |
| 5. C2×#13133140 | C2 | semidirect |
| 7. C2×#13133127 | C2 | semidirect |
| 8. C2×#107×C53 | C2 | semidirect |
| 12. C2×#11719913 | C4 | semidirect |
| 16. #13133182 | C22 | semidirect |
| 23. #13133140 | C22 | semidirect |
| 25. #13133127 | C22 | semidirect |
| 29. #107×C53 | C22 | semidirect |
| 45. C2×Dic106 | C2×C4 | semidirect |
| 47. C2×C8×C53 | C2×C4 | semidirect |
| 60. #11719913 | C2×C4 | semidirect |
| 86. Dic106 | C22×C4 | semidirect |
| 87. C8×C53 | C22×C4 | semidirect |
| 106. C2×C53 | #440 | semidirect |
| 115. C2×#107 | D53 | semidirect |
| 119. C53 | C2×#440 | semidirect |
| 137. #107 | C2×D53 | semidirect |
| 161. C2×C8 | C4×D53 | semidirect |
| 199. C8 | C2×C4×D53 | semidirect |
| 217. C2 | #16810722 | direct (N × H) |