Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
786 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 153 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×#386 | C2 |
| prime radical | C2×#10597383 | C2 |
| hypercenter | #386 | D19 |
| hypocenter | C19 | #2411 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597381 | C2 | semidirect |
| 3. C2×#10597323 | C2 | semidirect |
| 4. C22×(C2×D19)⋊C4 | C2 | semidirect |
| 5. #11926468 | C2 | semidirect |
| 6. #11926459 | C2 | semidirect |
| 7. #11926444 | C2 | semidirect |
| 8. #11926433 | C2 | semidirect |
| 9. #11926417 | C2 | semidirect |
| 10. #11926399 | C2 | semidirect |
| 11. C19×#386 | C2 | semidirect |
| 18. C2×C22⋊C4×C19 | C22 | semidirect |
| 21. C2×C22⋊Dic19 | C22 | semidirect |
| 22. C2×C22⋊Dic19 | C22 | semidirect |
| 31. C2×Dic19⋊C4 | C22 | semidirect |
| 32. C2×Dic19⋊C4 | C22 | semidirect |
| 33. C2×Dic19⋊C4 | C22 | semidirect |
| 34. C2×Dic19⋊C4 | C22 | semidirect |
| 35. C2×C4×Dic19 | C22 | semidirect |
| 37. C19×#95 | C22 | semidirect |
| 38. C19⋊#95 | C22 | semidirect |
| 60. C22×Dic19 | D4 | semidirect |
| 171. #386 | D19 | semidirect |
| 205. C2×C22⋊C4 | C2×D19 | semidirect |
| 208. #95 | C2×D19 | semidirect |
| 209. C19 | #2411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597381 | 2 |
| C2×#10597383 | 2 |
| C2×#10597323 | 2 |
| C22×(C2×D19)⋊C4 | 2 |
| #11926468 | 2 |
| #11926459 | 2 |
| #11926444 | 2 |
| #11926433 | 2 |
| #11926417 | 2 |
| #11926399 | 2 |
| C19×#386 | 2 |
| #2411 | 19 |