Finite Group DatabasebetaFinite Group DatabasebetaOrder 10432.
428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D163 |
| commutator, socle, cosocle | C22×C163 | C24 |
| Fitting | #121×C163 | C2 |
| hypercenter | #121 | D163 |
| hypocenter | C163 | D42 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D652 | C2 | semidirect |
| 2. C2×D4×D163 | C2 | semidirect |
| 3. C2×D4×D163 | C2 | semidirect |
| 4. #19104731 | C2 | semidirect |
| 5. #19104710 | C2 | semidirect |
| 6. #19104708 | C2 | semidirect |
| 7. #19104705 | C2 | semidirect |
| 8. #19104703 | C2 | semidirect |
| 9. #19104697 | C2 | semidirect |
| 10. C4×C22⋊D163 | C2 | semidirect |
| 11. #121×C163 | C2 | semidirect |
| 12. C23×D163 | C22 | semidirect |
| 13. C23×D163 | C22 | semidirect |
| 16. C2×D652 | C22 | semidirect |
| 17. C2×D652 | C22 | semidirect |
| 18. C2×D652 | C22 | semidirect |
| 20. C2×C22⋊D163 | C22 | semidirect |
| 21. C2×C22⋊D163 | C22 | semidirect |
| 22. C2×C22⋊D163 | C22 | semidirect |
| 25. C2×C4×D163 | C22 | semidirect |
| 26. C2×C4×D163 | C22 | semidirect |
| 27. Dic163⋊C4 | C22 | semidirect |
| 28. C22⋊Dic163 | C22 | semidirect |
| 29. (C2×D163)⋊C4 | C22 | semidirect |
| 30. (C2×D163)⋊C4 | C22 | semidirect |
| 31. (C2×D163)⋊C4 | C22 | semidirect |
| 32. C4×Dic163 | C22 | semidirect |
| 33. C2×D4×C163 | C22 | semidirect |
| 34. C2×D4×C163 | C22 | semidirect |
| 35. C22×C4×C163 | C22 | semidirect |
| 36. C4⋊C4×C163 | C22 | semidirect |
| 37. C22⋊C4×C163 | C22 | semidirect |
| 50. D652 | D4 | semidirect |
| 54. C22⋊D163 | D4 | semidirect |
| 73. C22×C163 | C2×D4 | semidirect |
| 84. C2×D163 | C2×D4 | semidirect |
| 85. C2×D163 | C2×D4 | semidirect |
| 88. C4×C163 | C2×D4 | semidirect |
| 91. Dic163 | C2×D4 | semidirect |
| 100. C163 | D42 | semidirect |
| 108. #121 | D163 | semidirect |
| 126. C2×D4 | C2×D163 | semidirect |
| 127. C2×D4 | C2×D163 | semidirect |
| 130. C22×C4 | C2×D163 | semidirect |
| 132. C4⋊C4 | C2×D163 | semidirect |
| 137. C22⋊C4 | C2×D163 | semidirect |
| 185. C22 | D4×D163 | semidirect |
| 192. C4 | D4×D163 | semidirect |