Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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×#13133243 | C2 | semidirect |
| 2. C4×#11719945 | C2 | semidirect |
| 3. #16810820 | C2 | semidirect |
| 4. #16810815 | C2 | semidirect |
| 5. #16810647 | C2 | semidirect |
| 6. #16810628 | C2 | semidirect |
| 7. C2×#127×C53 | C2 | semidirect |
| 10. C2×#11719923 | C22 | semidirect |
| 11. C2×#11719922 | C22 | semidirect |
| 13. C4×Dic106 | C22 | semidirect |
| 14. C4×D212 | C22 | semidirect |
| 19. C4⋊#88322 | C22 | semidirect |
| 20. #13133138 | C22 | semidirect |
| 39. #11719945 | D4 | semidirect |
| 78. D212 | C2×D4 | semidirect |
| 82. Dic106 | C2×D4 | semidirect |
| 94. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 106. C2×#127 | D53 | semidirect |
| 112. C53 | #3038 | semidirect |
| 201. C4 | #13133243 | semidirect |