Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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×C19 | C23 |
| hypercenter | #393 | D19 |
| hypocenter | C19 | #2821 |
| 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×#10597390 | C2 | semidirect |
| 3. #11926486 | C2 | semidirect |
| 5. #11926478 | C2 | semidirect |
| 7. #11926465 | C2 | semidirect |
| 8. #11926463 | C2 | semidirect |
| 10. #11926411 | C2 | semidirect |
| 162. C19 | #2821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597390 | 2 |
| C2×#10597325 | 2 |
| #11926486 | 2 |
| #11926480 | 2 |
| #11926478 | 2 |
| #11926472 | 2 |
| #11926465 | 2 |
| #11926463 | 2 |
| #11926456 | 2 |
| #11926411 | 2 |
| C19×#393 | 2 |
| #2821 | 19 |