Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133247 | C2 | semidirect |
| 2. C2×#13133242 | C2 | semidirect |
| 3. C22×#11719913 | C2 | semidirect |
| 4. #16811194 | C2 | semidirect |
| 5. #16811187 | C2 | semidirect |
| 6. #16811016 | C2 | semidirect |
| 7. #16811011 | C2 | semidirect |
| 8. #16811004 | C2 | semidirect |
| 9. #16810994 | C2 | semidirect |
| 10. #16810578 | C2 | semidirect |
| 11. C2×#135×C53 | C2 | semidirect |
| 16. C2×#11719925 | C22 | semidirect |
| 20. C2×#11719923 | C22 | semidirect |
| 24. #13133215 | C22 | semidirect |
| 27. #13133204 | C22 | semidirect |
| 33. #13133127 | C22 | semidirect |
| 34. C8×Dic53 | C22 | semidirect |
| 38. C2×Q16×C53 | C22 | semidirect |
| 39. C2×SD16×C53 | C22 | semidirect |
| 40. C2×SD16×C53 | C22 | semidirect |
| 41. C2×D8×C53 | C22 | semidirect |
| 71. C2×C8×C53 | D4 | semidirect |
| 84. #11719917 | D4 | semidirect |
| 151. C2×#135 | D53 | semidirect |
| 160. C53 | #3154 | semidirect |
| 169. C2×Q16 | C2×D53 | semidirect |
| 175. C2×SD16 | C2×D53 | semidirect |
| 176. C2×SD16 | C2×D53 | semidirect |
| 178. C2×D8 | C2×D53 | semidirect |
| 228. C2×C8 | C22⋊D53 | semidirect |