Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13133245 | C2 | semidirect |
| 3. #16811173 | C2 | semidirect |
| 4. C2×#13133205 | C2 | semidirect |
| 5. #16811017 | C2 | semidirect |
| 6. #16811012 | C2 | semidirect |
| 7. #16811007 | C2 | semidirect |
| 8. C4×M16×C53 | C2 | semidirect |
| 14. C2×Dic212 | C22 | semidirect |
| 16. C2×#11719913 | C22 | semidirect |
| 18. #13133217 | C22 | semidirect |
| 19. #13133214 | C22 | semidirect |
| 23. #13133205 | C22 | semidirect |
| 29. #97×C53 | C22 | semidirect |
| 30. C4×C8×C53 | C22 | semidirect |
| 48. M16×C53 | D4 | semidirect |
| 114. C4×M16 | D53 | semidirect |
| 115. C53 | #3153 | semidirect |
| 136. #97 | C2×D53 | semidirect |
| 137. C4×C8 | C2×D53 | semidirect |
| 159. M16 | D212 | semidirect |