Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
192 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 93 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×D313 |
| commutator, socle, cosocle | C22×C313 | C24 |
| Fitting | #126×C313 | C2 |
| prime radical | C23×C313 | C23 |
| hypercenter | #126 | D313 |
| hypocenter | C313 | #541 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23756496 | C2 | semidirect |
| 5. #23756489 | C2 | semidirect |
| 6. #23756488 | C2 | semidirect |
| 7. #23756487 | C2 | semidirect |
| 8. #23756487 | C2 | semidirect |
| 9. #23756487 | C2 | semidirect |
| 12. C4×Dic626 | C2 | semidirect |
| 13. #23756462 | C2 | semidirect |
| 91. C313 | #541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756496 | 2 |
| #23756490 | 2 |
| #23756489 | 2 |
| #23756488 | 2 |
| #23756487 | 2 |
| #23756474 | 2 |
| C4×Dic626 | 2 |
| #23756462 | 2 |
| #23756453 | 2 |
| #126×C313 | 2 |
| #541 | 313 |