Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D212 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#436 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #436 | D53 |
| hypocenter | C53 | #3273 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133245 | C2 | semidirect |
| 2. #16811269 | C2 | semidirect |
| 3. #16811007 | C2 | semidirect |
| 4. #16810869 | C2 | semidirect |
| 5. #16810839 | C2 | semidirect |
| 6. #16810787 | C2 | semidirect |
| 7. #16810759 | C2 | semidirect |
| 8. C4×D424 | C2 | semidirect |
| 9. C53×#436 | C2 | semidirect |
| 11. C22×D212 | C22 | semidirect |
| 13. C2×Dic212 | C22 | semidirect |
| 14. C2×#11719913 | C22 | semidirect |
| 15. C2×#11719913 | C22 | semidirect |
| 19. #13133205 | C22 | semidirect |
| 21. #13133196 | C22 | semidirect |
| 25. C4×D212 | C22 | semidirect |
| 27. #13133151 | C22 | semidirect |
| 28. #13133142 | C22 | semidirect |
| 29. #13133139 | C22 | semidirect |
| 30. #13133139 | C22 | semidirect |
| 31. C2×M16×C53 | C22 | semidirect |
| 33. C4⋊C8×C53 | C22 | semidirect |
| 34. C22⋊C8×C53 | C22 | semidirect |
| 35. C4×C8×C53 | C22 | semidirect |
| 68. D424 | D4 | semidirect |
| 133. #436 | D53 | semidirect |
| 134. C53 | #3273 | semidirect |
| 144. C2×M16 | C2×D53 | semidirect |
| 155. C4⋊C8 | C2×D53 | semidirect |
| 159. C22⋊C8 | C2×D53 | semidirect |
| 160. C4×C8 | C2×D53 | semidirect |