Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#384 | C2 |
| socle, cosocle | C23×C19 | C24 |
| prime radical | C22×D76 | C22 |
| hypercenter | #384 | D19 |
| hypocenter | C19 | #2326 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#10597333 | C2 | semidirect |
| 4. #11926449 | C2 | semidirect |
| 6. #11926434 | C2 | semidirect |
| 7. #11926415 | C2 | semidirect |
| 8. #11926390 | C2 | semidirect |
| 9. C19×#384 | C2 | semidirect |
| 26. #10597321 | C4 | semidirect |
| 46. C2×Dic38 | C2×C4 | semidirect |
| 50. C42×C19 | C2×C4 | semidirect |
| 53. (C2×D19)⋊C4 | C2×C4 | semidirect |
| 113. #384 | D19 | semidirect |
| 141. C19 | #2326 | semidirect |
| 169. C42 | C4×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597321 | 2 |
| C2×#10597333 | 2 |
| C2×#10597339 | 2 |
| #11926449 | 2 |
| #11926445 | 2 |
| #11926434 | 2 |
| #11926415 | 2 |
| #11926390 | 2 |
| C19×#384 | 2 |
| #2326 | 19 |