Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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×#13133132 | C2 | semidirect |
| 3. #16810415 | C2 | direct (N × H) |
| 4. C2×#99×C53 | C2 | semidirect |
| 5. C22×D212 | C4 | semidirect |
| 10. #13133213 | C4 | semidirect |
| 13. C2×C4×Dic53 | C4 | semidirect |
| 15. #13133132 | C22 | semidirect |
| 19. #99×C53 | C22 | semidirect |
| 42. C2×D212 | C2×C4 | semidirect |
| 48. C4×Dic53 | C2×C4 | semidirect |
| 118. C2×C53 | #353 | semidirect |
| 123. C2×#99 | D53 | semidirect |
| 125. C53 | C2×#353 | semidirect |
| 140. #99 | C2×D53 | semidirect |
| 239. C2 | #16810415 | direct (N × H) |