Finite Group DatabasebetaFinite Group DatabasebetaOrder 10048.
212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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×D157 |
| commutator, socle, cosocle | C22×C157 | C24 |
| Fitting | #126×C157 | C2 |
| prime radical | C2×C22⋊D157 | C22 |
| hypercenter | #126 | D157 |
| hypocenter | C157 | #556 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19097770 | C2 | semidirect |
| 2. #19097766 | C2 | semidirect |
| 3. #19097766 | C2 | semidirect |
| 4. #19097764 | C2 | semidirect |
| 7. #19097749 | C2 | semidirect |
| 8. #19097748 | C2 | semidirect |
| 9. C4×Dic314 | C2 | semidirect |
| 10. #19097736 | C2 | semidirect |
| 11. #19097736 | C2 | semidirect |
| 13. #19097728 | C2 | semidirect |
| 14. #19097727 | C2 | semidirect |
| 15. #126×C157 | C2 | semidirect |
| 97. C157 | #556 | semidirect |
| 103. #126 | D157 | semidirect |