Finite Group DatabasebetaFinite Group DatabasebetaOrder 10432.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C22×D4×C163 | C2 |
| hypercenter | C22×D4 | D163 |
| hypocenter | C163 | #534 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D163 | C2 | semidirect |
| 2. #19104718 | C2 | semidirect |
| 3. #19104716 | C2 | semidirect |
| 4. #19104707 | C2 | semidirect |
| 5. #19104704 | C2 | semidirect |
| 6. #19104703 | C2 | semidirect |
| 7. C2×C22⋊Dic163 | C2 | semidirect |
| 8. C22×D4×C163 | C2 | semidirect |
| 9. C23×D163 | C22 | semidirect |
| 12. C2×C22⋊D163 | C22 | semidirect |
| 13. C2×C22⋊D163 | C22 | semidirect |
| 14. C22×Dic163 | C22 | semidirect |
| 15. C22×Dic163 | C22 | semidirect |
| 16. Dic163⋊C4 | C22 | semidirect |
| 17. C22⋊Dic163 | C22 | semidirect |
| 18. C22⋊Dic163 | C22 | semidirect |
| 19. C22⋊Dic163 | C22 | semidirect |
| 20. (C2×D163)⋊C4 | C22 | semidirect |
| 22. C24×C163 | C22 | semidirect |
| 25. C2×D4×C163 | C22 | semidirect |
| 26. C22×C4×C163 | C22 | semidirect |
| 40. C23×C163 | D4 | semidirect |
| 73. C163 | #534 | semidirect |
| 76. C22×D4 | D163 | semidirect |
| 85. C24 | C2×D163 | semidirect |
| 92. C2×D4 | C2×D163 | semidirect |
| 95. C22×C4 | C2×D163 | semidirect |
| 107. C23 | C22⋊D163 | semidirect |