Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
932 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 157 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 | C2×C19×#127 | C2 |
| hypercenter | C2×#127 | D19 |
| hypocenter | C19 | #2669 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597385 | C2 | semidirect |
| 2. C2×#10597383 | C2 | semidirect |
| 3. C2×#10597383 | C2 | semidirect |
| 4. #11926458 | C2 | semidirect |
| 5. #11926452 | C2 | semidirect |
| 6. #11926452 | C2 | semidirect |
| 7. #11926435 | C2 | semidirect |
| 8. #11926424 | C2 | semidirect |
| 9. C2×C19×#127 | C2 | semidirect |
| 13. C22×D4×C19 | C22 | semidirect |
| 14. C22×D4×C19 | C22 | semidirect |
| 18. C23×Dic19 | C22 | semidirect |
| 20. C2×C42×C19 | C22 | semidirect |
| 23. C2×C22⋊Dic19 | C22 | semidirect |
| 24. C2×C22⋊Dic19 | C22 | semidirect |
| 25. C2×C22⋊Dic19 | C22 | semidirect |
| 32. C2×Dic19⋊C4 | C22 | semidirect |
| 33. C19⋊#95 | C22 | semidirect |
| 34. C19⋊#95 | C22 | semidirect |
| 55. C2×D4×C19 | D4 | semidirect |
| 80. (C2×D19)⋊C4 | D4 | semidirect |
| 171. C2×#127 | D19 | semidirect |
| 195. C22×D4 | C2×D19 | semidirect |
| 196. C22×D4 | C2×D19 | semidirect |
| 211. C2×C42 | C2×D19 | semidirect |
| 214. C19 | #2669 | semidirect |
| 244. C2×D4 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597385 | 2 |
| C2×#10597383 | 2 |
| #11926458 | 2 |
| #11926452 | 2 |
| #11926435 | 2 |
| #11926424 | 2 |
| C2×C19×#127 | 2 |
| #2669 | 19 |