Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #11927024 | C2 | semidirect |
| 3. #11926867 | C2 | semidirect |
| 4. #11926866 | C2 | semidirect |
| 5. #11926861 | C2 | semidirect |
| 6. #11926856 | C2 | semidirect |
| 7. #11926586 | C2 | semidirect |
| 8. #11926580 | C2 | semidirect |
| 9. C2×#10597289 | C2 | semidirect |
| 10. #11926512 | C2 | semidirect |
| 11. C19×#418 | C2 | semidirect |
| 24. #10597338 | C22 | semidirect |
| 25. C4⋊C4×D19 | C22 | semidirect |
| 33. (C2×D19)⋊C8 | C22 | semidirect |
| 34. (C2×D19)⋊C8 | C22 | semidirect |
| 35. #10597275 | C22 | semidirect |
| 36. #10597274 | C22 | semidirect |
| 37. #10597265 | C22 | semidirect |
| 38. #10597265 | C22 | semidirect |
| 39. #10597264 | C22 | semidirect |
| 40. #10597264 | C22 | semidirect |
| 137. #418 | D19 | semidirect |
| 175. C19 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927111 | 2 |
| #11927024 | 2 |
| #11926867 | 2 |
| #11926866 | 2 |
| #11926861 | 2 |
| #11926856 | 2 |
| #11926586 | 2 |
| #11926580 | 2 |
| C2×#10597289 | 2 |
| #11926512 | 2 |
| C19×#418 | 2 |
| #3096 | 19 |