Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 121 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×#393 | C2 |
| prime radical | C24×D19 | C22 |
| hypercenter | #393 | D19 |
| hypocenter | C19 | #2736 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11926473 | C2 | semidirect |
| 2. #11926469 | C2 | semidirect |
| 3. #11926455 | C2 | semidirect |
| 4. #11926438 | C2 | semidirect |
| 5. #11926436 | C2 | semidirect |
| 6. #11926433 | C2 | semidirect |
| 9. C19×#393 | C2 | semidirect |
| 11. C22×Q8×C19 | C22 | semidirect |
| 22. C2×C4⋊Dic19 | C22 | semidirect |
| 23. C2×Dic19⋊C4 | C22 | semidirect |
| 24. C2×C4×Dic19 | C22 | semidirect |
| 25. C19×#95 | C22 | semidirect |
| 26. C19×#95 | C22 | semidirect |
| 27. C19⋊#95 | C22 | semidirect |
| 28. C19⋊#95 | C22 | semidirect |
| 29. C19⋊#95 | C22 | semidirect |
| 30. C19⋊#95 | C22 | semidirect |
| 127. #393 | D19 | semidirect |
| 141. C22×Q8 | C2×D19 | semidirect |
| 159. #95 | C2×D19 | semidirect |
| 160. #95 | C2×D19 | semidirect |
| 161. C19 | #2736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11926473 | 2 |
| #11926469 | 2 |
| #11926455 | 2 |
| #11926438 | 2 |
| #11926436 | 2 |
| #11926433 | 2 |
| #11926399 | 2 |
| C19×#393 | 2 |
| #2736 | 19 |