Finite Group DatabasebetaFinite Group DatabasebetaOrder 19904.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×D311 |
| commutator, socle, cosocle | C22×C311 | C24 |
| Fitting | #126×C311 | C2 |
| prime radical | C2×C22⋊D311 | C22 |
| hypercenter | #126 | D311 |
| hypocenter | C311 | #563 |
| LCS | G ▷ C22×C311 ▷ C311 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23755708 | C2 | semidirect |
| 2. #23755707 | C2 | semidirect |
| 3. #23755703 | C2 | semidirect |
| 4. #23755702 | C2 | semidirect |
| 5. #23755701 | C2 | semidirect |
| 6. #23755699 | C2 | semidirect |
| 7. #23755698 | C2 | semidirect |
| 11. #23755688 | C2 | semidirect |
| 12. #23755686 | C2 | semidirect |
| 13. #23755685 | C2 | semidirect |
| 14. #23755685 | C2 | semidirect |
| 15. #126×C311 | C2 | semidirect |
| 97. C311 | #563 | semidirect |
| 104. #126 | D311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23755708 | 2 |
| #23755707 | 2 |
| #23755703 | 2 |
| #23755702 | 2 |
| #23755701 | 2 |
| #23755699 | 2 |
| #23755698 | 2 |
| #23755694 | 2 |
| #23755692 | 2 |
| #23755690 | 2 |
| #23755688 | 2 |
| #23755686 | 2 |
| #23755685 | 2 |
| #126×C311 | 2 |
| #563 | 311 |