Finite Group DatabasebetaFinite Group DatabasebetaOrder 10048.
330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 330 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×D157 |
| commutator, socle, cosocle | C22×C157 | C24 |
| Fitting | #120×C157 | C2 |
| hypercenter | #120 | D157 |
| hypocenter | C157 | #525 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14578953 | C2 | semidirect |
| 2. C23×Dic157 | C2 | semidirect |
| 3. #19097755 | C2 | semidirect |
| 4. #19097752 | C2 | semidirect |
| 5. #19097748 | C2 | semidirect |
| 6. #19097743 | C2 | semidirect |
| 7. #19097740 | C2 | semidirect |
| 8. D4×Dic157 | C2 | semidirect |
| 9. #19097731 | C2 | semidirect |
| 10. #19097727 | C2 | semidirect |
| 11. #120×C157 | C2 | semidirect |
| 13. C2×Dic314 | C22 | semidirect |
| 16. C2×C22⋊D157 | C22 | semidirect |
| 22. C22×Dic157 | C22 | semidirect |
| 23. C2×C4×D157 | C22 | semidirect |
| 24. C4⋊Dic157 | C22 | semidirect |
| 25. #14578933 | C22 | semidirect |
| 26. #14578933 | C22 | semidirect |
| 29. C22⋊Dic157 | C22 | semidirect |
| 30. #14578931 | C22 | semidirect |
| 31. C4×Dic157 | C22 | semidirect |
| 46. C2×Dic157 | D4 | semidirect |
| 69. C22×C157 | #41 | semidirect |
| 86. C157 | #525 | semidirect |
| 95. #120 | D157 | semidirect |
| 158. C22 | #14578953 | semidirect |