Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D157 |
| commutator, socle, cosocle | C22×C157 | C25 |
| Frattini | C22 | C24×D157 |
| Fitting | C22×C42×C157 | C2 |
| hypercenter | C22×C42 | D157 |
| hypocenter | C157 | #3444 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23757830 | C2 | semidirect |
| 2. #23757823 | C2 | semidirect |
| 3. #23757807 | C2 | semidirect |
| 4. #23757784 | C2 | semidirect |
| 5. C4×#14578954 | C2 | semidirect |
| 6. C22×C42×C157 | C2 | semidirect |
| 8. #19097771 | C22 | semidirect |
| 9. #19097768 | C22 | semidirect |
| 10. #19097765 | C22 | semidirect |
| 11. #19097763 | C22 | semidirect |
| 12. #19097759 | C22 | semidirect |
| 17. C4×Dic314 | C22 | semidirect |
| 18. C4×D628 | C22 | semidirect |
| 21. #19097728 | C22 | semidirect |
| 22. C42×D157 | C22 | semidirect |
| 60. C2×C4×C157 | #41 | semidirect |
| 76. C157 | #3444 | semidirect |
| 83. C22×C42 | D157 | semidirect |
| 137. C2×C4 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| #23757823 | 2 |
| #23757807 | 2 |
| #23757784 | 2 |
| C4×#14578954 | 2 |
| C22×C42×C157 | 2 |
| #3444 | 157 |