Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927357 | C2 | semidirect |
| 2. #11927346 | C2 | semidirect |
| 3. #11926986 | C2 | semidirect |
| 4. #11926982 | C2 | semidirect |
| 5. #11926981 | C2 | semidirect |
| 6. #11926977 | C2 | semidirect |
| 7. #11926974 | C2 | semidirect |
| 8. C2×#10597285 | C2 | semidirect |
| 9. SD32×D19 | C2 | semidirect |
| 10. #11926962 | C2 | semidirect |
| 11. C19×#510 | C2 | semidirect |
| 15. C2×Q16×C19 | C22 | semidirect |
| 19. #10597365 | C22 | semidirect |
| 21. Q16×D19 | C22 | semidirect |
| 24. #10597350 | C22 | semidirect |
| 27. C19×Q32 | C22 | semidirect |
| 28. C19×SD32 | C22 | semidirect |
| 29. C19×M32 | C22 | semidirect |
| 30. #10597286 | C22 | semidirect |
| 31. #10597285 | C22 | semidirect |
| 32. #10597285 | C22 | semidirect |
| 33. #10597285 | C22 | semidirect |
| 34. #10597284 | C22 | semidirect |
| 35. #10597283 | C22 | semidirect |
| 36. C2×C19⋊C16 | C22 | semidirect |
| 37. #10597257 | C22 | semidirect |
| 38. D304 | C22 | semidirect |
| 39. #10597255 | C22 | semidirect |
| 40. C16×D19 | C22 | semidirect |
| 124. #510 | D19 | semidirect |
| 149. C2×Q16 | C2×D19 | semidirect |
| 154. Q32 | C2×D19 | semidirect |
| 160. SD32 | C2×D19 | semidirect |
| 164. M32 | C2×D19 | semidirect |
| 167. C19 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927357 | 2 |
| #11927346 | 2 |
| #11926986 | 2 |
| #11926982 | 2 |
| #11926981 | 2 |
| #11926977 | 2 |
| #11926974 | 2 |
| C2×#10597285 | 2 |
| SD32×D19 | 2 |
| #11926962 | 2 |
| C19×#510 | 2 |
| #3416 | 19 |