Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
814 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 157 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×#381 | C2 |
| prime radical | C2×#10597328 | C2 |
| hypercenter | #381 | D19 |
| hypocenter | C19 | #2412 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597375 | C2 | semidirect |
| 3. C22×(C2×D19)⋊C4 | C2 | semidirect |
| 4. C2×C22⋊C4×D19 | C2 | semidirect |
| 5. #11926473 | C2 | semidirect |
| 6. #11926462 | C2 | semidirect |
| 7. #11926422 | C2 | semidirect |
| 8. #11926421 | C2 | semidirect |
| 9. #11926416 | C2 | semidirect |
| 10. #11926403 | C2 | semidirect |
| 11. C19×#381 | C2 | semidirect |
| 29. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 30. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 31. C2×Dic19⋊C4 | C22 | semidirect |
| 32. C2×Dic19⋊C4 | C22 | semidirect |
| 35. C19×#95 | C22 | semidirect |
| 36. C19×#95 | C22 | semidirect |
| 37. C19⋊#95 | C22 | semidirect |
| 38. C19⋊#95 | C22 | semidirect |
| 72. C22⋊Dic19 | D4 | semidirect |
| 159. C2×D19 | #123 | semidirect |
| 176. #381 | D19 | semidirect |
| 212. #95 | C2×D19 | semidirect |
| 213. #95 | C2×D19 | semidirect |
| 214. C19 | #2412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597375 | 2 |
| C2×#10597328 | 2 |
| C22×(C2×D19)⋊C4 | 2 |
| C2×C22⋊C4×D19 | 2 |
| #11926473 | 2 |
| #11926462 | 2 |
| #11926422 | 2 |
| #11926421 | 2 |
| #11926416 | 2 |
| #11926403 | 2 |
| C19×#381 | 2 |
| #2412 | 19 |