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×#391 | C2 |
| socle, cosocle | C23×C19 | C24 |
| prime radical | C22×D76 | C22 |
| hypercenter | #391 | D19 |
| hypocenter | C19 | #2326 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic19 | C2 | semidirect |
| 5. #11926433 | C2 | semidirect |
| 6. #11926418 | C2 | semidirect |
| 7. #11926413 | C2 | semidirect |
| 8. #11926390 | C2 | semidirect |
| 9. C19×#391 | C2 | semidirect |
| 15. #10597393 | C4 | semidirect |
| 33. C2×Q8×C19 | C2×C4 | semidirect |
| 51. (C2×D19)⋊C4 | C2×C4 | semidirect |
| 56. C4×Dic19 | C2×C4 | semidirect |
| 109. #391 | D19 | semidirect |
| 141. C19 | #2326 | semidirect |
| 145. C2×Q8 | C4×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597393 | 2 |
| C2×Q8×Dic19 | 2 |
| C2×#10597339 | 2 |
| #11926446 | 2 |
| #11926433 | 2 |
| #11926418 | 2 |
| #11926413 | 2 |
| #11926390 | 2 |
| C19×#391 | 2 |
| #2326 | 19 |