Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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. #16811064 | C2 | semidirect |
| 3. C2×#13133160 | C2 | semidirect |
| 4. #16810435 | C2 | semidirect |
| 5. #16810429 | C2 | semidirect |
| 6. #16810407 | C2 | semidirect |
| 7. C53×#473 | C2 | semidirect |
| 18. #13133157 | C22 | semidirect |
| 19. C2×#11719908 | C22 | semidirect |
| 21. C2×Q16×C53 | C22 | semidirect |
| 23. #108×C53 | C22 | semidirect |
| 95. #473 | D53 | semidirect |
| 99. C53 | #2194 | semidirect |
| 106. C2×Q16 | C2×D53 | semidirect |
| 115. #108 | C2×D53 | semidirect |