Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#13133248 | C2 | semidirect |
| 3. C2×Q8×Dic53 | C2 | semidirect |
| 4. #16810847 | C2 | semidirect |
| 5. #16810843 | C2 | semidirect |
| 6. #16810831 | C2 | semidirect |
| 7. #16810821 | C2 | semidirect |
| 8. #16810646 | C2 | semidirect |
| 9. #16810625 | C2 | semidirect |
| 10. #16810624 | C2 | semidirect |
| 11. C2×#137×C53 | C2 | semidirect |
| 49. C2×Q8×C53 | D4 | semidirect |
| 150. Dic53 | #137 | semidirect |
| 159. C2×#137 | D53 | semidirect |
| 169. C53 | #3037 | semidirect |
| 210. C2×Q8 | C22⋊D53 | semidirect |