Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10597396 | C2 | semidirect |
| 2. #11927111 | C2 | semidirect |
| 3. #11927027 | C2 | semidirect |
| 4. #11926764 | C2 | semidirect |
| 5. #11926757 | C2 | semidirect |
| 6. #11926742 | C2 | semidirect |
| 7. #11926737 | C2 | semidirect |
| 8. #11926572 | C2 | semidirect |
| 9. #11926546 | C2 | semidirect |
| 10. C2×#10597289 | C2 | semidirect |
| 11. C2×C19×AGL(1,ℤ/8) | C2 | semidirect |
| 21. Q8×Dic19 | C22 | semidirect |
| 22. C2×#64528 | C22 | semidirect |
| 23. C2×#64527 | C22 | semidirect |
| 29. D4×Dic19 | C22 | semidirect |
| 30. C2×#64526 | C22 | semidirect |
| 31. C2×#64525 | C22 | semidirect |
| 39. #10597278 | C22 | semidirect |
| 40. #10597273 | C22 | semidirect |
| 41. Dic19⋊C8 | C22 | semidirect |
| 42. Dic19⋊C8 | C22 | semidirect |
| 45. #41×C19 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D19 | semidirect |
| 197. C19 | #3045 | semidirect |
| 202. #41 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597396 | 2 |
| #11927111 | 2 |
| #11927027 | 2 |
| #11926764 | 2 |
| #11926757 | 2 |
| #11926742 | 2 |
| #11926737 | 2 |
| #11926572 | 2 |
| #11926546 | 2 |
| C2×#10597289 | 2 |
| C2×C19×AGL(1,ℤ/8) | 2 |
| #3045 | 19 |