Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
688 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D19 |
| commutator, socle, cosocle | C23×C19 | C24 |
| Fitting | C19×#386 | C2 |
| prime radical | C2×#10597383 | C2 |
| hypercenter | #386 | D19 |
| hypocenter | C19 | #2684 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597382 | C2 | semidirect |
| 3. #11926469 | C2 | semidirect |
| 4. #11926460 | C2 | semidirect |
| 5. #11926457 | C2 | semidirect |
| 6. #11926436 | C2 | semidirect |
| 7. #11926423 | C2 | semidirect |
| 8. #11926399 | C2 | semidirect |
| 9. C19×#386 | C2 | semidirect |
| 12. C23×C4×C19 | C22 | semidirect |
| 14. C22×Dic38 | C22 | semidirect |
| 16. C2×C22⋊C4×C19 | C22 | semidirect |
| 19. C2×C22⋊Dic19 | C22 | semidirect |
| 27. C2×C4⋊Dic19 | C22 | semidirect |
| 28. C2×C4×Dic19 | C22 | semidirect |
| 29. C19×#95 | C22 | semidirect |
| 30. C19⋊#95 | C22 | semidirect |
| 31. C19⋊#95 | C22 | semidirect |
| 32. C19⋊#95 | C22 | semidirect |
| 152. #386 | D19 | semidirect |
| 166. C23×C4 | C2×D19 | semidirect |
| 179. C2×C22⋊C4 | C2×D19 | semidirect |
| 184. #95 | C2×D19 | semidirect |
| 185. C19 | #2684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597382 | 2 |
| C2×#10597383 | 2 |
| #11926469 | 2 |
| #11926460 | 2 |
| #11926457 | 2 |
| #11926436 | 2 |
| #11926423 | 2 |
| #11926399 | 2 |
| C19×#386 | 2 |
| #2684 | 19 |