Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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. #16810734 | C2 | direct (N × H) |
| 4. C2×#13133137 | C2 | semidirect |
| 5. C2×#13133127 | C2 | semidirect |
| 6. C2×#106×C53 | C2 | semidirect |
| 9. C2×D424 | C4 | semidirect |
| 13. #13133179 | C22 | semidirect |
| 16. #13133137 | C22 | semidirect |
| 17. #13133127 | C22 | semidirect |
| 20. #106×C53 | C22 | semidirect |
| 27. C2×D212 | C2×C4 | semidirect |
| 31. C2×C8×C53 | C2×C4 | semidirect |
| 40. D424 | C2×C4 | semidirect |
| 56. D212 | C22×C4 | semidirect |
| 58. C8×C53 | C22×C4 | semidirect |
| 73. C2×C53 | #442 | semidirect |
| 80. C2×#106 | D53 | semidirect |
| 83. C53 | C2×#442 | semidirect |
| 95. #106 | C2×D53 | semidirect |
| 111. C2×C8 | C4×D53 | semidirect |
| 136. C8 | C2×C4×D53 | semidirect |
| 150. C2 | #16810734 | direct (N × H) |