Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 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. #127×D19 | C2 | semidirect |
| 2. #11927073 | C2 | semidirect |
| 3. #11926934 | C2 | semidirect |
| 4. #11926909 | C2 | semidirect |
| 5. #11926908 | C2 | semidirect |
| 6. #11926742 | C2 | semidirect |
| 7. #11926737 | C2 | semidirect |
| 8. #11926693 | C2 | semidirect |
| 9. #11926676 | C2 | semidirect |
| 10. #11926599 | C2 | semidirect |
| 11. C19×#496 | C2 | semidirect |
| 15. C2×SD16×C19 | C22 | semidirect |
| 16. C2×D8×C19 | C22 | semidirect |
| 18. C19×#124 | C22 | semidirect |
| 20. Q8×Dic19 | C22 | semidirect |
| 21. C2×#64527 | C22 | semidirect |
| 26. D4×Dic19 | C22 | semidirect |
| 27. C2×#64525 | C22 | semidirect |
| 34. #10597316 | C22 | semidirect |
| 35. C19×#97 | C22 | semidirect |
| 36. #10597289 | C22 | semidirect |
| 37. #10597289 | C22 | semidirect |
| 38. #10597278 | C22 | semidirect |
| 39. #10597278 | C22 | semidirect |
| 41. Dic19⋊C8 | C22 | semidirect |
| 42. #10597260 | C22 | semidirect |
| 149. #496 | D19 | semidirect |
| 168. C2×SD16 | C2×D19 | semidirect |
| 170. C2×D8 | C2×D19 | semidirect |
| 178. #124 | C2×D19 | semidirect |
| 194. #97 | C2×D19 | semidirect |
| 195. C19 | #3217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D19 | 2 |
| #11927073 | 2 |
| #11926934 | 2 |
| #11926909 | 2 |
| #11926908 | 2 |
| #11926742 | 2 |
| #11926737 | 2 |
| #11926693 | 2 |
| #11926676 | 2 |
| #11926599 | 2 |
| C19×#496 | 2 |
| #3217 | 19 |