Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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×#13133179 | C2 | semidirect |
| 3. #16810705 | C2 | direct (N × H) |
| 4. C2×#13133137 | C2 | semidirect |
| 5. C2×C8×Dic53 | C2 | semidirect |
| 6. C2×#107×C53 | C2 | semidirect |
| 9. C2×D424 | C4 | semidirect |
| 13. #13133179 | C22 | semidirect |
| 16. #13133137 | C22 | semidirect |
| 17. C8×Dic53 | C22 | semidirect |
| 20. #107×C53 | C22 | semidirect |
| 28. C2×D212 | C2×C4 | semidirect |
| 32. C2×C8×C53 | C2×C4 | semidirect |
| 41. D424 | C2×C4 | semidirect |
| 54. C2×Dic53 | D8 | semidirect |
| 59. D212 | C22×C4 | semidirect |
| 61. C8×C53 | C22×C4 | semidirect |
| 76. Dic53 | C2×D8 | semidirect |
| 78. C2×C53 | C4×D8 | semidirect |
| 86. C2×#107 | D53 | semidirect |
| 89. C53 | C2×C4×D8 | semidirect |
| 101. #107 | C2×D53 | semidirect |
| 118. C2×C8 | C4×D53 | semidirect |
| 145. C8 | C2×C4×D53 | semidirect |
| 161. C2 | #16810705 | direct (N × H) |