Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D53 |
| commutator | C4×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#442 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #442 | D53 |
| hypocenter | C53 | C2×#442 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×D4×D53 | C2 | semidirect |
| 3. #16810736 | C2 | semidirect |
| 4. #16810735 | C2 | semidirect |
| 5. #16810734 | C2 | semidirect |
| 6. #16810733 | C2 | semidirect |
| 7. #16810732 | C2 | semidirect |
| 8. #106×D53 | C2 | semidirect |
| 9. #102×D53 | C2 | semidirect |
| 10. #97×D53 | C2 | semidirect |
| 11. C53×#442 | C2 | semidirect |
| 16. D8×D53 | C4 | semidirect |
| 19. C4×D212 | C22 | semidirect |
| 20. D4×Dic53 | C22 | semidirect |
| 21. #13133179 | C22 | semidirect |
| 27. #13133149 | C22 | semidirect |
| 28. #13133148 | C22 | semidirect |
| 29. #13133139 | C22 | semidirect |
| 30. #13133138 | C22 | semidirect |
| 31. #13133137 | C22 | semidirect |
| 32. #13133128 | C22 | semidirect |
| 33. #13133127 | C22 | semidirect |
| 34. #13133127 | C22 | semidirect |
| 36. C4×D4×C53 | C22 | semidirect |
| 37. #106×C53 | C22 | semidirect |
| 38. #102×C53 | C22 | semidirect |
| 39. #97×C53 | C22 | semidirect |
| 46. D4×D53 | C2×C4 | semidirect |
| 54. D8×C53 | C2×C4 | semidirect |
| 61. #11719922 | C2×C4 | semidirect |
| 70. D424 | C2×C4 | semidirect |
| 72. C8×D53 | C2×C4 | semidirect |
| 80. D4×C53 | C22×C4 | semidirect |
| 91. D212 | C22×C4 | semidirect |
| 99. C8×C53 | C22×C4 | semidirect |
| 101. #88322 | C22×C4 | semidirect |
| 124. D53 | #442 | direct (N × H) |
| 132. #442 | D53 | direct (N × H) |
| 136. C53 | C2×#442 | semidirect |
| 150. C4×D4 | C2×D53 | semidirect |
| 156. #106 | C2×D53 | semidirect |
| 160. #102 | C2×D53 | semidirect |
| 164. #97 | C2×D53 | semidirect |
| 181. D8 | C4×D53 | semidirect |
| 208. D4 | C2×C4×D53 | semidirect |
| 226. C8 | C2×C4×D53 | semidirect |