Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11927089 | C2 | semidirect |
| 2. C2×#10597386 | C2 | semidirect |
| 3. #11926919 | C2 | semidirect |
| 4. #11926889 | C2 | semidirect |
| 5. #11926738 | C2 | semidirect |
| 6. #11926737 | C2 | semidirect |
| 7. #11926680 | C2 | semidirect |
| 8. #11926678 | C2 | semidirect |
| 9. #11926677 | C2 | semidirect |
| 10. #11926594 | C2 | semidirect |
| 11. C19×#447 | C2 | semidirect |
| 17. C2×D8×C19 | C22 | semidirect |
| 23. #10597386 | C22 | semidirect |
| 25. D4×Dic19 | C22 | semidirect |
| 26. C2×#64525 | C22 | semidirect |
| 27. C2×#64525 | C22 | semidirect |
| 30. C2×D152 | C22 | semidirect |
| 31. #10597339 | C22 | semidirect |
| 32. #10597334 | C22 | semidirect |
| 35. C19×#102 | C22 | semidirect |
| 37. #10597289 | C22 | semidirect |
| 39. #10597278 | C22 | semidirect |
| 40. Dic19⋊C8 | C22 | semidirect |
| 41. C8×Dic19 | C22 | semidirect |
| 42. #10597266 | C22 | semidirect |
| 117. C2×Dic19 | D8 | semidirect |
| 166. #447 | D19 | semidirect |
| 184. C2×D8 | C2×D19 | semidirect |
| 203. #102 | C2×D19 | semidirect |
| 207. C19 | #3205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927089 | 2 |
| C2×#10597386 | 2 |
| #11926919 | 2 |
| #11926889 | 2 |
| #11926738 | 2 |
| #11926737 | 2 |
| #11926680 | 2 |
| #11926678 | 2 |
| #11926677 | 2 |
| #11926594 | 2 |
| C19×#447 | 2 |
| #3205 | 19 |