Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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×#393 | C2 |
| prime radical | C24×D19 | C22 |
| hypercenter | #393 | D19 |
| hypocenter | C19 | #2561 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597392 | C2 | semidirect |
| 3. #11926471 | C2 | semidirect |
| 4. #11926469 | C2 | semidirect |
| 5. #11926455 | C2 | semidirect |
| 6. #11926433 | C2 | semidirect |
| 7. #11926432 | C2 | semidirect |
| 8. #11926406 | C2 | semidirect |
| 10. #11926391 | C2 | semidirect |
| 11. C19×#393 | C2 | semidirect |
| 13. C22×Q8×C19 | C22 | semidirect |
| 27. C2×C4⋊Dic19 | C22 | semidirect |
| 28. C2×Dic19⋊C4 | C22 | semidirect |
| 29. C2×C4×Dic19 | C22 | semidirect |
| 31. C19×#95 | C22 | semidirect |
| 32. C19×#95 | C22 | semidirect |
| 33. C19⋊#95 | C22 | semidirect |
| 34. C19⋊#95 | C22 | semidirect |
| 35. C19⋊#95 | C22 | semidirect |
| 36. C19⋊#95 | C22 | semidirect |
| 151. #393 | D19 | semidirect |
| 166. C22×Q8 | C2×D19 | semidirect |
| 188. #95 | C2×D19 | semidirect |
| 189. #95 | C2×D19 | semidirect |
| 190. C19 | #2561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597392 | 2 |
| C2×C22⋊C4×D19 | 2 |
| #11926471 | 2 |
| #11926469 | 2 |
| #11926455 | 2 |
| #11926433 | 2 |
| #11926432 | 2 |
| #11926406 | 2 |
| #11926399 | 2 |
| #11926391 | 2 |
| C19×#393 | 2 |
| #2561 | 19 |