Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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 | #3324 |
| 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. #16811343 | C2 | semidirect |
| 3. #16810970 | C2 | semidirect |
| 4. #16810948 | C2 | semidirect |
| 5. #16810904 | C2 | semidirect |
| 6. #16810869 | C2 | semidirect |
| 7. #16810824 | C2 | semidirect |
| 8. #16810776 | C2 | semidirect |
| 9. C4×#11719913 | C2 | semidirect |
| 10. #16810629 | C2 | semidirect |
| 11. C53×#436 | C2 | semidirect |
| 15. C2×#11719913 | C22 | semidirect |
| 16. #13133217 | C22 | semidirect |
| 20. #13133196 | C22 | semidirect |
| 24. C4×Dic106 | C22 | semidirect |
| 27. #13133176 | C22 | semidirect |
| 28. #13133151 | C22 | semidirect |
| 29. #13133149 | C22 | semidirect |
| 30. #13133142 | C22 | semidirect |
| 33. #13133139 | C22 | semidirect |
| 34. #13133139 | C22 | semidirect |
| 35. #13133139 | C22 | semidirect |
| 36. C2×M16×C53 | C22 | semidirect |
| 38. C4⋊C8×C53 | C22 | semidirect |
| 39. C22⋊C8×C53 | C22 | semidirect |
| 40. C4×C8×C53 | C22 | semidirect |
| 145. #436 | D53 | semidirect |
| 147. C53 | #3324 | semidirect |
| 152. C2×M16 | C2×D53 | semidirect |
| 168. C4⋊C8 | C2×D53 | semidirect |
| 175. C22⋊C8 | C2×D53 | semidirect |
| 176. C4×C8 | C2×D53 | semidirect |