Finite Group DatabasebetaFinite Group DatabasebetaOrder 10432.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #562 |
| 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. #19104725 | C2 | semidirect |
| 2. #19104722 | C2 | semidirect |
| 3. #19104721 | C2 | semidirect |
| 4. #19104718 | C2 | semidirect |
| 5. #19104717 | C2 | semidirect |
| 6. #19104716 | C2 | semidirect |
| 7. #19104716 | C2 | semidirect |
| 8. #19104714 | C2 | semidirect |
| 9. #19104713 | C2 | semidirect |
| 10. #19104712 | C2 | semidirect |
| 11. #19104712 | C2 | semidirect |
| 12. #19104707 | C2 | semidirect |
| 13. #19104707 | C2 | semidirect |
| 14. #19104706 | C2 | semidirect |
| 15. #121×C163 | C2 | semidirect |
| 109. C163 | #562 | semidirect |
| 125. #121 | D163 | semidirect |