Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 145 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×Q16×D19 | C2 | semidirect |
| 2. C2×SD16×D19 | C2 | semidirect |
| 4. #124×D19 | C2 | semidirect |
| 5. #11926929 | C2 | semidirect |
| 6. #11926928 | C2 | semidirect |
| 7. #11926927 | C2 | semidirect |
| 8. #11926926 | C2 | semidirect |
| 9. #11926925 | C2 | semidirect |
| 10. C4×C8×D19 | C2 | semidirect |
| 11. C19×#495 | C2 | semidirect |
| 14. C2×Q16×C19 | C22 | semidirect |
| 15. C2×SD16×C19 | C22 | semidirect |
| 17. C19×#124 | C22 | semidirect |
| 18. #10597393 | C22 | semidirect |
| 19. C2×#64528 | C22 | semidirect |
| 20. C2×#64527 | C22 | semidirect |
| 21. #10597382 | C22 | semidirect |
| 22. C2×#64526 | C22 | semidirect |
| 27. C2×Dic76 | C22 | semidirect |
| 29. C2×#64516 | C22 | semidirect |
| 34. #10597321 | C22 | semidirect |
| 36. C4×C8×C19 | C22 | semidirect |
| 37. C8×Dic19 | C22 | semidirect |
| 38. C8×Dic19 | C22 | semidirect |
| 39. C4×C19⋊C8 | C22 | semidirect |
| 131. #495 | D19 | direct (N × H) |
| 137. D19 | #495 | direct (N × H) |
| 143. C2×Q16 | C2×D19 | semidirect |
| 148. C2×SD16 | C2×D19 | semidirect |
| 159. #124 | C2×D19 | semidirect |
| 165. C4×C8 | C2×D19 | semidirect |
| 166. C19 | C2×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D19 | 2 |
| C2×SD16×D19 | 2 |
| C2×D8×D19 | 2 |
| #124×D19 | 2 |
| #11926929 | 2 |
| #11926928 | 2 |
| #11926927 | 2 |
| #11926926 | 2 |
| #11926925 | 2 |
| C4×C8×D19 | 2 |
| C19×#495 | 2 |
| C2×#495 | 19 |