Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
504 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 193 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 | C22×C19 | C23×C4 |
| Fitting | C19×#380 | C2 |
| socle, cosocle | C23×C19 | C24 |
| prime radical | C24×C19 | C23 |
| hypercenter | #380 | D19 |
| hypocenter | C19 | #2347 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11926440 | C2 | semidirect |
| 4. #11926411 | C2 | semidirect |
| 5. C4⋊C4×Dic19 | C2 | semidirect |
| 6. #11926395 | C2 | semidirect |
| 14. #10597372 | C4 | semidirect |
| 120. C19 | #2347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597372 | 2 |
| #11926440 | 2 |
| #11926432 | 2 |
| #11926411 | 2 |
| C4⋊C4×Dic19 | 2 |
| #11926395 | 2 |
| C4×C22⋊Dic19 | 2 |
| C19×#380 | 2 |
| #2347 | 19 |