Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
534 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 534 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×#395 | C2 |
| prime radical | #11926454 | C2 |
| hypercenter | #395 | D19 |
| hypocenter | C19 | #2662 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597344 | C2 | semidirect |
| 2. C2×#10597393 | C2 | semidirect |
| 3. #11926466 | C2 | semidirect |
| 4. #11926462 | C2 | semidirect |
| 5. #11926461 | C2 | semidirect |
| 6. #11926455 | C2 | semidirect |
| 8. #11926445 | C2 | semidirect |
| 9. #11926433 | C2 | semidirect |
| 10. #11926395 | C2 | semidirect |
| 11. C19×#395 | C2 | semidirect |
| 70. C4×Dic19 | D4 | semidirect |
| 140. #395 | D19 | semidirect |
| 180. C19 | #2662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597344 | 2 |
| C2×#10597393 | 2 |
| #11926466 | 2 |
| #11926462 | 2 |
| #11926461 | 2 |
| #11926455 | 2 |
| #11926454 | 2 |
| #11926445 | 2 |
| #11926433 | 2 |
| #11926395 | 2 |
| C19×#395 | 2 |
| #2662 | 19 |