Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 119 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×#10597339 | C2 | semidirect |
| 3. #11926862 | C2 | semidirect |
| 4. #11926847 | C2 | semidirect |
| 5. #11926762 | C2 | semidirect |
| 6. #11926694 | C2 | semidirect |
| 8. #11926629 | C2 | semidirect |
| 9. #11926626 | C2 | semidirect |
| 10. #11926594 | C2 | semidirect |
| 11. C19×#484 | C2 | semidirect |
| 16. #10597393 | C22 | semidirect |
| 17. Q8×Dic19 | C22 | semidirect |
| 28. #10597339 | C22 | semidirect |
| 30. #10597336 | C22 | semidirect |
| 33. C19×#107 | C22 | semidirect |
| 34. C19×#103 | C22 | semidirect |
| 38. Dic19⋊C8 | C22 | semidirect |
| 39. C8×Dic19 | C22 | semidirect |
| 41. #10597266 | C22 | semidirect |
| 42. #10597265 | C22 | semidirect |
| 137. #484 | D19 | semidirect |
| 173. #107 | C2×D19 | semidirect |
| 176. #103 | C2×D19 | semidirect |
| 183. C19 | #3105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927080 | 2 |
| C2×#10597339 | 2 |
| #11926862 | 2 |
| #11926847 | 2 |
| #11926762 | 2 |
| #11926694 | 2 |
| #11926680 | 2 |
| #11926629 | 2 |
| #11926626 | 2 |
| #11926594 | 2 |
| C19×#484 | 2 |
| #3105 | 19 |