Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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×Q8×D53 | C2 | semidirect |
| 2. C2×#13133246 | C2 | semidirect |
| 4. #16810781 | C2 | semidirect |
| 5. #16810780 | C2 | semidirect |
| 6. #16810779 | C2 | semidirect |
| 7. #16810761 | C2 | semidirect |
| 8. #16810760 | C2 | semidirect |
| 9. #16810630 | C2 | semidirect |
| 10. #16810585 | C2 | semidirect |
| 11. C53×#448 | C2 | semidirect |
| 23. C2×Dic212 | C22 | semidirect |
| 24. C2×#11719925 | C22 | semidirect |
| 25. C2×#11719923 | C22 | semidirect |
| 35. #13133142 | C22 | semidirect |
| 36. #13133141 | C22 | semidirect |
| 37. #13133140 | C22 | semidirect |
| 41. C2×SD16×C53 | C22 | semidirect |
| 43. #103×C53 | C22 | semidirect |
| 63. Q8×D53 | D4 | semidirect |
| 144. C22×C53 | #137 | semidirect |
| 152. C2×D53 | #137 | semidirect |
| 178. #448 | D53 | semidirect |
| 181. C53 | #3004 | semidirect |
| 197. C2×SD16 | C2×D53 | semidirect |
| 211. #103 | C2×D53 | semidirect |
| 321. C22 | #13133246 | semidirect |