Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #16811389 | C2 | semidirect |
| 3. #16810629 | C2 | semidirect |
| 4. #16810627 | C2 | semidirect |
| 5. #16810596 | C2 | semidirect |
| 6. #16810379 | C2 | semidirect |
| 7. C53×H(3,ℤ/4) | C2 | semidirect |
| 14. #13133214 | C4 | semidirect |
| 15. #13133205 | C4 | semidirect |
| 44. C2×C8×C53 | D4 | semidirect |
| 57. C2×#88322 | D4 | semidirect |
| 122. H(3,ℤ/4) | D53 | semidirect |
| 123. C53 | #1910 | semidirect |
| 165. C2×C8 | D212 | semidirect |