Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 147 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 | C22×C22⋊D19 | C22 |
| hypercenter | #393 | D19 |
| hypocenter | C19 | #2398 |
| 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×Q8×Dic19 | C2 | semidirect |
| 3. #11926486 | C2 | semidirect |
| 4. #11926471 | C2 | semidirect |
| 5. #11926469 | C2 | semidirect |
| 7. #11926455 | C2 | semidirect |
| 8. C22⋊C4×Dic19 | C2 | semidirect |
| 9. #11926391 | C2 | semidirect |
| 10. #11926389 | C2 | semidirect |
| 11. C19×#393 | C2 | semidirect |
| 139. #393 | D19 | semidirect |
| 175. C19 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic19 | 2 |
| C2×(C22⋊D19)⋊C4 | 2 |
| #11926486 | 2 |
| #11926471 | 2 |
| #11926469 | 2 |
| #11926460 | 2 |
| #11926455 | 2 |
| C22⋊C4×Dic19 | 2 |
| #11926391 | 2 |
| #11926389 | 2 |
| C19×#393 | 2 |
| #2398 | 19 |