Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#11719947 | C2 | semidirect |
| 2. C2×#13133247 | C2 | semidirect |
| 3. #16811130 | C2 | semidirect |
| 4. #16810782 | C2 | semidirect |
| 5. #16810765 | C2 | semidirect |
| 6. #16810633 | C2 | semidirect |
| 7. #16810628 | C2 | semidirect |
| 8. #16810586 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 19. C2×#11719925 | C22 | semidirect |
| 20. C2×#11719923 | C22 | semidirect |
| 23. #13133193 | C22 | semidirect |
| 24. #13133188 | C22 | semidirect |
| 28. #13133142 | C22 | semidirect |
| 29. #13133138 | C22 | semidirect |
| 30. #13133129 | C22 | semidirect |
| 34. C2×SD16×C53 | C22 | semidirect |
| 35. C2×D8×C53 | C22 | semidirect |
| 45. C2×D4×C53 | D4 | semidirect |
| 66. C2×Dic106 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 155. C53 | #3005 | semidirect |
| 170. C2×SD16 | C2×D53 | semidirect |
| 171. C2×D8 | C2×D53 | semidirect |
| 201. C2×D4 | C22⋊D53 | semidirect |