Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11927057 | C2 | semidirect |
| 2. C2×#10597384 | C2 | semidirect |
| 3. #11926877 | C2 | semidirect |
| 4. #11926867 | C2 | semidirect |
| 5. #11926863 | C2 | semidirect |
| 6. #11926779 | C2 | semidirect |
| 7. #11926770 | C2 | semidirect |
| 8. #11926688 | C2 | semidirect |
| 9. #11926678 | C2 | semidirect |
| 10. C22⋊C8×D19 | C2 | semidirect |
| 11. C19×#450 | C2 | semidirect |
| 14. C2×#64545 | C22 | semidirect |
| 16. C2×SD16×C19 | C22 | semidirect |
| 19. #10597392 | C22 | semidirect |
| 24. C2×#64525 | C22 | semidirect |
| 27. C2×C8×D19 | C22 | semidirect |
| 28. #10597341 | C22 | semidirect |
| 31. #10597338 | C22 | semidirect |
| 34. C19×#102 | C22 | semidirect |
| 36. #10597292 | C22 | semidirect |
| 37. #10597289 | C22 | semidirect |
| 39. #10597278 | C22 | semidirect |
| 40. (C2×D19)⋊C8 | C22 | semidirect |
| 41. #10597274 | C22 | semidirect |
| 42. #10597264 | C22 | semidirect |
| 158. #450 | D19 | semidirect |
| 174. C2×SD16 | C2×D19 | semidirect |
| 197. #102 | C2×D19 | semidirect |
| 201. C19 | #3188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927057 | 2 |
| C2×#10597384 | 2 |
| #11926877 | 2 |
| #11926867 | 2 |
| #11926863 | 2 |
| #11926779 | 2 |
| #11926770 | 2 |
| #11926688 | 2 |
| #11926678 | 2 |
| C22⋊C8×D19 | 2 |
| C19×#450 | 2 |
| #3188 | 19 |