Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 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×#10597435 | C2 | semidirect |
| 2. #11927349 | C2 | direct (N × H) |
| 3. C2×#10597354 | C2 | semidirect |
| 4. C2×#10597350 | C2 | semidirect |
| 5. C22×D152 | C2 | semidirect |
| 6. C2×C19×#131 | C2 | semidirect |
| 9. #10597435 | C22 | semidirect |
| 12. C2×#64541 | C22 | semidirect |
| 13. C22×D76 | C22 | semidirect |
| 14. C19×#131 | C22 | semidirect |
| 15. C2×M16×C19 | C22 | semidirect |
| 16. C22×C8×C19 | C22 | semidirect |
| 17. #10597354 | C22 | semidirect |
| 18. C2×Dic76 | C22 | semidirect |
| 19. #10597350 | C22 | semidirect |
| 20. C2×D152 | C22 | semidirect |
| 21. C2×D152 | C22 | semidirect |
| 22. C2×D152 | C22 | semidirect |
| 23. C2×#64516 | C22 | semidirect |
| 34. #64541 | C23 | semidirect |
| 38. C2×D76 | C23 | semidirect |
| 41. M16×C19 | C23 | semidirect |
| 44. C2×C8×C19 | C23 | semidirect |
| 45. Dic76 | C23 | semidirect |
| 46. D152 | C23 | semidirect |
| 47. D152 | C23 | semidirect |
| 48. #64516 | C23 | semidirect |
| 85. C2×#131 | D19 | semidirect |
| 87. C2×C19 | #576 | semidirect |
| 104. #131 | C2×D19 | semidirect |
| 105. C2×M16 | C2×D19 | semidirect |
| 106. C22×C8 | C2×D19 | semidirect |
| 107. C19 | C2×#576 | semidirect |
| 129. M16 | C22×D19 | semidirect |
| 132. C2×C8 | C22×D19 | semidirect |
| 165. C2 | #11927349 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597435 | 2 |
| #11927349 | 2 |
| C2×#10597354 | 2 |
| C2×#10597350 | 2 |
| C22×D152 | 2 |
| C2×C19×#131 | 2 |
| C2×#576 | 19 |