Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
546 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#10597357 | C2 | semidirect |
| 2. #11927198 | C2 | semidirect |
| 3. #11927179 | C2 | semidirect |
| 4. #11926916 | C2 | semidirect |
| 5. #11926789 | C2 | semidirect |
| 6. #11926750 | C2 | semidirect |
| 7. #11926696 | C2 | semidirect |
| 8. #11926686 | C2 | semidirect |
| 9. C4×#64525 | C2 | semidirect |
| 10. #11926621 | C2 | semidirect |
| 11. C19×#459 | C2 | semidirect |
| 12. C2×#64543 | C22 | semidirect |
| 15. C2×D8×C19 | C22 | semidirect |
| 17. C4×D4×C19 | C22 | semidirect |
| 21. C2×#64526 | C22 | semidirect |
| 22. C2×#64526 | C22 | semidirect |
| 28. C2×#64515 | C22 | semidirect |
| 29. #10597343 | C22 | semidirect |
| 33. #10597315 | C22 | semidirect |
| 34. C19×C4⋊C8 | C22 | semidirect |
| 35. C19×#102 | C22 | semidirect |
| 36. #10597289 | C22 | semidirect |
| 37. (C2×D19)⋊C8 | C22 | semidirect |
| 38. #10597273 | C22 | semidirect |
| 40. #10597264 | C22 | semidirect |
| 41. C4×C19⋊C8 | C22 | semidirect |
| 70. #64525 | D4 | semidirect |
| 95. D4×C19 | C2×D4 | semidirect |
| 118. C19⋊C8 | C2×D4 | semidirect |
| 136. C4×C19 | AGL(1,ℤ/8) | semidirect |
| 148. #459 | D19 | semidirect |
| 168. C2×D8 | C2×D19 | semidirect |
| 180. C4×D4 | C2×D19 | semidirect |
| 183. C4⋊C8 | C2×D19 | semidirect |
| 187. #102 | C2×D19 | semidirect |
| 190. C19 | #3272 | semidirect |
| 252. D4 | D4×D19 | semidirect |
| 287. C4 | #10597357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597357 | 2 |
| #11927198 | 2 |
| #11927179 | 2 |
| #11926916 | 2 |
| #11926789 | 2 |
| #11926750 | 2 |
| #11926696 | 2 |
| #11926686 | 2 |
| C4×#64525 | 2 |
| #11926621 | 2 |
| C19×#459 | 2 |
| #3272 | 19 |