Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
852 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 169 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×#10597385 | C2 |
| hypercenter | #386 | D19 |
| hypocenter | C19 | #2436 |
| 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. C23×Dic38 | C2 | semidirect |
| 2. C2×#10597331 | C2 | semidirect |
| 4. #11926457 | C2 | semidirect |
| 5. #11926456 | C2 | semidirect |
| 6. #11926448 | C2 | semidirect |
| 7. #11926424 | C2 | semidirect |
| 8. #11926423 | C2 | semidirect |
| 9. #11926421 | C2 | semidirect |
| 10. C22⋊C4×Dic19 | C2 | semidirect |
| 11. C19×#386 | C2 | semidirect |
| 70. C2×Dic38 | D4 | semidirect |
| 137. C22×C19 | #124 | semidirect |
| 165. #386 | D19 | semidirect |
| 202. C19 | #2436 | semidirect |
| 305. C22 | #10597331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic38 | 2 |
| C2×#10597331 | 2 |
| C2×#10597385 | 2 |
| #11926457 | 2 |
| #11926456 | 2 |
| #11926448 | 2 |
| #11926424 | 2 |
| #11926423 | 2 |
| #11926421 | 2 |
| C22⋊C4×Dic19 | 2 |
| C19×#386 | 2 |
| #2436 | 19 |