Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic106 | C2 | semidirect |
| 3. #16810723 | C2 | direct (N × H) |
| 4. C2×#13133150 | C2 | semidirect |
| 5. C2×#13133140 | C2 | semidirect |
| 7. C2×#13133128 | C2 | semidirect |
| 10. C2×#11719923 | C4 | semidirect |
| 15. C4×Dic106 | C22 | semidirect |
| 19. #13133150 | C22 | semidirect |
| 20. #13133140 | C22 | semidirect |
| 22. #13133128 | C22 | semidirect |
| 45. C2×Dic106 | C2×C4 | semidirect |
| 52. #11719923 | C2×C4 | semidirect |
| 58. C2×#88322 | C2×C4 | semidirect |
| 86. Dic106 | C22×C4 | semidirect |
| 88. #88322 | C22×C4 | semidirect |
| 107. C2×C53 | #440 | semidirect |
| 119. C53 | C2×#440 | semidirect |
| 217. C2 | #16810723 | direct (N × H) |