Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D19 |
| commutator, cosocle | C4×C19 | C25 |
| Frattini | C4 | C24×D19 |
| Fitting | C19×#585 | C2 |
| socle | C2×C19 | C23×D4 |
| hypercenter | #585 | D19 |
| hypocenter | C19 | #3586 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597436 | C2 | semidirect |
| 2. #11927359 | C2 | semidirect |
| 3. #11927355 | C2 | semidirect |
| 4. #11927342 | C2 | semidirect |
| 5. C2×#10597397 | C2 | semidirect |
| 6. #11927311 | C2 | semidirect |
| 7. C19×#585 | C2 | semidirect |
| 9. C19×2−1+4 | C22 | semidirect |
| 11. C19×H(5,𝔽2) | C22 | semidirect |
| 16. #10597436 | C22 | semidirect |
| 19. C2×#64541 | C22 | semidirect |
| 20. C22×Dic38 | C22 | semidirect |
| 21. #10597397 | C22 | semidirect |
| 22. #10597397 | C22 | semidirect |
| 23. #10597396 | C22 | semidirect |
| 24. #10597395 | C22 | semidirect |
| 25. #10597394 | C22 | semidirect |
| 26. C2×#64528 | C22 | semidirect |
| 27. #10597388 | C22 | semidirect |
| 28. C2×#64526 | C22 | semidirect |
| 29. #10597378 | C22 | semidirect |
| 30. C2×#64520 | C22 | semidirect |
| 108. #585 | D19 | semidirect |
| 123. 2−1+4 | C2×D19 | semidirect |
| 125. H(5,𝔽2) | C2×D19 | semidirect |
| 143. C19 | #3586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597436 | 2 |
| #11927359 | 2 |
| #11927355 | 2 |
| #11927342 | 2 |
| C2×#10597397 | 2 |
| #11927311 | 2 |
| C19×#585 | 2 |
| #3586 | 19 |