Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11927080 | C2 | semidirect |
| 2. C2×#10597382 | C2 | semidirect |
| 3. #11926925 | C2 | semidirect |
| 4. #11926897 | C2 | semidirect |
| 5. #11926764 | C2 | semidirect |
| 6. #11926758 | C2 | semidirect |
| 7. #11926699 | C2 | semidirect |
| 8. #11926685 | C2 | semidirect |
| 10. #11926594 | C2 | semidirect |
| 11. C19×#450 | C2 | semidirect |
| 18. #10597393 | C22 | semidirect |
| 19. Q8×Dic19 | C22 | semidirect |
| 20. C2×#64528 | C22 | semidirect |
| 28. C2×#64516 | C22 | semidirect |
| 30. #10597339 | C22 | semidirect |
| 32. #10597336 | C22 | semidirect |
| 39. #10597273 | C22 | semidirect |
| 40. Dic19⋊C8 | C22 | semidirect |
| 41. C8×Dic19 | C22 | semidirect |
| 42. #10597267 | C22 | semidirect |
| 145. #450 | D19 | semidirect |
| 186. C19 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927080 | 2 |
| C2×#10597382 | 2 |
| #11926925 | 2 |
| #11926897 | 2 |
| #11926764 | 2 |
| #11926758 | 2 |
| #11926699 | 2 |
| #11926685 | 2 |
| #11926678 | 2 |
| #11926594 | 2 |
| C19×#450 | 2 |
| #3211 | 19 |