Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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×#381 | C2 |
| hypercenter | #381 | D19 |
| hypocenter | C19 | #2613 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D76 | C2 | semidirect |
| 2. C2×#10597375 | C2 | semidirect |
| 3. C2×#10597328 | C2 | semidirect |
| 4. #11926462 | C2 | semidirect |
| 5. #11926454 | C2 | semidirect |
| 6. #11926399 | C2 | semidirect |
| 7. C19×#381 | C2 | semidirect |
| 14. C22×D76 | C22 | semidirect |
| 18. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 19. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 21. C2×Dic19⋊C4 | C22 | semidirect |
| 23. C19×#95 | C22 | semidirect |
| 28. C23×D19 | D4 | semidirect |
| 32. C22×C4×C19 | D4 | semidirect |
| 103. #381 | D19 | semidirect |
| 126. #95 | C2×D19 | semidirect |
| 127. C19 | #2613 | semidirect |
| 145. C22×C4 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D76 | 2 |
| C2×#10597375 | 2 |
| C2×#10597328 | 2 |
| #11926462 | 2 |
| #11926454 | 2 |
| #11926399 | 2 |
| C19×#381 | 2 |
| #2613 | 19 |