Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 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×D76 |
| commutator, cosocle | C4×C19 | C25 |
| Frattini | C4 | C24×D19 |
| Fitting | C19×#568 | C2 |
| socle | C2×C19 | C23×D4 |
| hypercenter | #568 | D19 |
| hypocenter | C19 | #3585 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927380 | C2 | semidirect |
| 2. C2×#10597435 | C2 | semidirect |
| 3. #11927356 | C2 | semidirect |
| 4. #11927349 | C2 | semidirect |
| 5. #11927344 | C2 | semidirect |
| 6. C2×#10597354 | C2 | semidirect |
| 7. C19×#568 | C2 | semidirect |
| 9. #10597436 | C22 | semidirect |
| 11. #10597435 | C22 | semidirect |
| 12. #10597435 | C22 | semidirect |
| 18. C2×#64541 | C22 | semidirect |
| 19. C2×#64541 | C22 | semidirect |
| 20. C22×D76 | C22 | semidirect |
| 21. C19×#131 | C22 | semidirect |
| 22. C2×M16×C19 | C22 | semidirect |
| 23. #10597355 | C22 | semidirect |
| 24. #10597355 | C22 | semidirect |
| 25. #10597354 | C22 | semidirect |
| 26. #10597354 | C22 | semidirect |
| 27. #10597354 | C22 | semidirect |
| 28. #10597350 | C22 | semidirect |
| 29. C2×D152 | C22 | semidirect |
| 30. C2×#64516 | C22 | semidirect |
| 50. #64541 | C23 | semidirect |
| 55. C2×D76 | C23 | semidirect |
| 59. C2×Dic38 | C23 | semidirect |
| 61. M16×C19 | C23 | semidirect |
| 62. C2×C8×C19 | C23 | semidirect |
| 63. Dic76 | C23 | semidirect |
| 64. D152 | C23 | semidirect |
| 65. #64516 | C23 | semidirect |
| 66. #64516 | C23 | semidirect |
| 116. #568 | D19 | semidirect |
| 143. #131 | C2×D19 | semidirect |
| 144. C2×M16 | C2×D19 | semidirect |
| 145. C19 | #3585 | semidirect |
| 180. M16 | C22×D19 | semidirect |
| 181. C2×C8 | C22×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927380 | 2 |
| C2×#10597435 | 2 |
| #11927356 | 2 |
| #11927349 | 2 |
| #11927344 | 2 |
| C2×#10597354 | 2 |
| C19×#568 | 2 |
| #3585 | 19 |