Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. M32×D53 | C2 | semidirect |
| 3. #16810658 | C2 | semidirect |
| 4. #16810434 | C2 | semidirect |
| 5. #16810433 | C2 | semidirect |
| 6. #16810432 | C2 | semidirect |
| 7. C53×#360 | C2 | semidirect |
| 9. #13133240 | C4 | semidirect |
| 13. #13133236 | C4 | semidirect |
| 14. Q16×D53 | C4 | semidirect |
| 16. D8×D53 | C4 | semidirect |
| 19. #13133157 | C22 | semidirect |
| 23. #13133149 | C22 | semidirect |
| 25. M32×C53 | C22 | semidirect |
| 26. #106×C53 | C22 | semidirect |
| 117. #360 | D53 | semidirect |
| 118. C53 | #2145 | semidirect |
| 133. M32 | C2×D53 | semidirect |
| 137. #106 | C2×D53 | semidirect |