Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13133128 | C2 | semidirect |
| 3. #16810362 | C2 | direct (N × H) |
| 4. C2×#97×C53 | C2 | semidirect |
| 15. #13133128 | C22 | semidirect |
| 19. #97×C53 | C22 | semidirect |
| 81. C2×C53 | #329 | semidirect |
| 88. C2×#97 | D53 | semidirect |
| 90. C53 | C2×#329 | semidirect |
| 105. #97 | C2×D53 | semidirect |
| 167. C2 | #16810362 | direct (N × H) |