Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 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×#379 | C2 |
| prime radical | C23×C22⋊D19 | C2 |
| hypercenter | #379 | D19 |
| hypocenter | C19 | #2405 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#10597332 | C2 | semidirect |
| 3. C22×C22⋊Dic19 | C2 | semidirect |
| 4. #11926460 | C2 | semidirect |
| 5. #11926421 | C2 | semidirect |
| 6. #11926419 | C2 | semidirect |
| 7. #11926399 | C2 | semidirect |
| 8. C19×#379 | C2 | semidirect |
| 16. C23×Dic19 | C22 | semidirect |
| 17. C23×Dic19 | C22 | semidirect |
| 19. C2×C22⋊C4×C19 | C22 | semidirect |
| 20. C2×C22⋊C4×C19 | C22 | semidirect |
| 23. C2×C22⋊Dic19 | C22 | semidirect |
| 24. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 25. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 26. C2×C4⋊Dic19 | C22 | semidirect |
| 28. C19⋊#95 | C22 | semidirect |
| 120. C22×C19 | #123 | semidirect |
| 142. #379 | D19 | semidirect |
| 168. C2×C22⋊C4 | C2×D19 | semidirect |
| 169. C2×C22⋊C4 | C2×D19 | semidirect |
| 171. C19 | #2405 | semidirect |
| 268. C22 | #10597332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D19 | 2 |
| C2×#10597332 | 2 |
| C22×C22⋊Dic19 | 2 |
| #11926460 | 2 |
| #11926421 | 2 |
| #11926419 | 2 |
| #11926399 | 2 |
| C19×#379 | 2 |
| #2405 | 19 |