Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×Q16×D19 | C2 | semidirect |
| 3. #11926987 | C2 | semidirect |
| 4. #11926986 | C2 | semidirect |
| 5. #11926985 | C2 | semidirect |
| 6. #11926984 | C2 | semidirect |
| 7. #11926983 | C2 | semidirect |
| 8. Q32×D19 | C2 | semidirect |
| 9. SD32×D19 | C2 | semidirect |
| 10. M32×D19 | C2 | semidirect |
| 11. C19×#510 | C2 | semidirect |
| 15. C2×Q16×C19 | C22 | semidirect |
| 23. Q16×D19 | C22 | semidirect |
| 28. C2×Dic76 | C22 | semidirect |
| 31. C19×Q32 | C22 | semidirect |
| 32. C19×SD32 | C22 | semidirect |
| 33. C19×M32 | C22 | semidirect |
| 34. #10597286 | C22 | semidirect |
| 35. #10597286 | C22 | semidirect |
| 36. #10597285 | C22 | semidirect |
| 37. #10597284 | C22 | semidirect |
| 38. #10597269 | C22 | semidirect |
| 39. Dic152 | C22 | semidirect |
| 40. #10597257 | C22 | semidirect |
| 41. #10597255 | C22 | semidirect |
| 146. #510 | D19 | direct (N × H) |
| 155. D19 | #510 | direct (N × H) |
| 171. C2×Q16 | C2×D19 | semidirect |
| 178. Q32 | C2×D19 | semidirect |
| 182. SD32 | C2×D19 | semidirect |
| 185. M32 | C2×D19 | semidirect |
| 187. C19 | C2×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D19 | 2 |
| C2×Q16×D19 | 2 |
| #11926987 | 2 |
| #11926986 | 2 |
| #11926985 | 2 |
| #11926984 | 2 |
| #11926983 | 2 |
| Q32×D19 | 2 |
| SD32×D19 | 2 |
| M32×D19 | 2 |
| C19×#510 | 2 |
| C2×#510 | 19 |