Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
668 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 149 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×#385 | C2 |
| prime radical | C24×D19 | C22 |
| hypercenter | #385 | D19 |
| hypocenter | C19 | #2626 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #385 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597324 | C2 | semidirect |
| 3. #11926479 | C2 | semidirect |
| 4. #11926468 | C2 | semidirect |
| 5. #11926466 | C2 | semidirect |
| 6. #11926457 | C2 | semidirect |
| 7. #11926417 | C2 | semidirect |
| 8. #11926402 | C2 | semidirect |
| 11. C19×#385 | C2 | semidirect |
| 15. C22×Dic38 | C22 | semidirect |
| 16. C2×C4⋊C4×C19 | C22 | semidirect |
| 28. C2×C4⋊Dic19 | C22 | semidirect |
| 29. C2×Dic19⋊C4 | C22 | semidirect |
| 30. C2×Dic19⋊C4 | C22 | semidirect |
| 31. C2×Dic19⋊C4 | C22 | semidirect |
| 32. C2×Dic19⋊C4 | C22 | semidirect |
| 34. C19×#95 | C22 | semidirect |
| 35. C19⋊#95 | C22 | semidirect |
| 36. C19⋊#95 | C22 | semidirect |
| 42. C23×D19 | Q8 | semidirect |
| 152. #385 | D19 | semidirect |
| 173. C2×C4⋊C4 | C2×D19 | semidirect |
| 187. #95 | C2×D19 | semidirect |
| 188. C19 | #2626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597324 | 2 |
| C22×(C2×D19)⋊C4 | 2 |
| #11926479 | 2 |
| #11926468 | 2 |
| #11926466 | 2 |
| #11926457 | 2 |
| #11926417 | 2 |
| #11926402 | 2 |
| #11926399 | 2 |
| C19×#385 | 2 |
| #2626 | 19 |