Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 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×#380 | C2 |
| prime radical | C24×D19 | C22 |
| hypercenter | #380 | D19 |
| hypocenter | C19 | #2626 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597370 | C2 | semidirect |
| 3. #11926481 | C2 | semidirect |
| 4. #11926466 | C2 | semidirect |
| 5. #11926457 | C2 | semidirect |
| 6. #11926419 | C2 | semidirect |
| 8. C19×#380 | C2 | semidirect |
| 12. C22×Dic38 | C22 | semidirect |
| 13. C2×C4⋊C4×C19 | C22 | semidirect |
| 21. C2×C4⋊Dic19 | C22 | semidirect |
| 22. C2×C4⋊Dic19 | C22 | semidirect |
| 24. C2×Dic19⋊C4 | C22 | semidirect |
| 25. C19×#95 | C22 | semidirect |
| 26. C19⋊#95 | C22 | semidirect |
| 32. C23×D19 | Q8 | semidirect |
| 117. #380 | D19 | semidirect |
| 134. C2×C4⋊C4 | C2×D19 | semidirect |
| 143. #95 | C2×D19 | semidirect |
| 144. C19 | #2626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597370 | 2 |
| C22×(C2×D19)⋊C4 | 2 |
| #11926481 | 2 |
| #11926466 | 2 |
| #11926457 | 2 |
| #11926419 | 2 |
| #11926399 | 2 |
| C19×#380 | 2 |
| #2626 | 19 |