Finite Group DatabasebetaFinite Group DatabasebetaOrder 10048.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #123×C157 | C2 |
| prime radical | C2×#14578953 | C2 |
| hypercenter | #123 | D157 |
| hypocenter | C157 | #536 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic314 | C2 | semidirect |
| 3. #19097770 | C2 | semidirect |
| 4. #19097757 | C2 | semidirect |
| 5. #19097755 | C2 | semidirect |
| 6. #19097754 | C2 | semidirect |
| 7. #19097752 | C2 | semidirect |
| 8. #19097749 | C2 | semidirect |
| 9. #19097748 | C2 | semidirect |
| 10. #19097727 | C2 | semidirect |
| 11. #123×C157 | C2 | semidirect |
| 79. C157 | #536 | semidirect |
| 88. #123 | D157 | semidirect |