Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 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. C2×#13133250 | C2 | semidirect |
| 2. C2×#13133247 | C2 | semidirect |
| 3. C2×#13133243 | C2 | semidirect |
| 4. #16811169 | C2 | semidirect |
| 5. C2×#13133204 | C2 | semidirect |
| 6. #16811014 | C2 | semidirect |
| 7. #16811011 | C2 | semidirect |
| 8. #16811006 | C2 | semidirect |
| 9. #16811004 | C2 | semidirect |
| 10. M16×Dic53 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 17. C2×Dic212 | C22 | semidirect |
| 18. C2×#11719925 | C22 | semidirect |
| 19. C2×#11719913 | C22 | semidirect |
| 21. C2×#11719923 | C22 | semidirect |
| 24. #13133215 | C22 | semidirect |
| 25. #13133213 | C22 | semidirect |
| 26. #13133206 | C22 | semidirect |
| 30. #13133204 | C22 | semidirect |
| 35. #13133127 | C22 | semidirect |
| 36. C8×Dic53 | C22 | semidirect |
| 70. M16×C53 | D4 | semidirect |
| 84. #11719917 | D4 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 162. C53 | #3153 | semidirect |
| 228. M16 | C22⋊D53 | semidirect |