Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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×#390 | C2 |
| prime radical | C22×D4×C19 | C22 |
| hypercenter | #390 | D19 |
| hypocenter | C19 | #2644 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11926472 | C2 | semidirect |
| 2. #11926472 | C2 | semidirect |
| 3. #11926469 | C2 | semidirect |
| 4. #11926467 | C2 | semidirect |
| 7. #11926443 | C2 | semidirect |
| 8. #11926442 | C2 | semidirect |
| 9. #11926440 | C2 | semidirect |
| 10. #11926390 | C2 | semidirect |
| 170. C19 | #2644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11926472 | 2 |
| #11926469 | 2 |
| #11926467 | 2 |
| #11926447 | 2 |
| #11926443 | 2 |
| #11926442 | 2 |
| #11926440 | 2 |
| #11926390 | 2 |
| C19×#390 | 2 |
| #2644 | 19 |