Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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. #106×D53 | 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 |
| 22. #13133149 | C22 | semidirect |
| 25. M32×C53 | C22 | semidirect |
| 26. #106×C53 | C22 | semidirect |
| 39. Q16×C53 | C2×C4 | semidirect |
| 41. D8×C53 | C2×C4 | semidirect |
| 51. Dic212 | C2×C4 | semidirect |
| 52. D424 | C2×C4 | semidirect |
| 111. D53 | #360 | direct (N × H) |
| 118. #360 | D53 | direct (N × H) |
| 119. C53 | C2×#360 | semidirect |
| 134. M32 | C2×D53 | semidirect |
| 138. #106 | C2×D53 | semidirect |
| 153. Q16 | C4×D53 | semidirect |
| 160. D8 | C4×D53 | semidirect |