Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 556 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 |
|---|---|---|
| 1. C2×#10597357 | C2 | semidirect |
| 2. #11927214 | C2 | semidirect |
| 3. #11927179 | C2 | semidirect |
| 4. #11926794 | C2 | semidirect |
| 5. #11926741 | C2 | semidirect |
| 6. #11926736 | C2 | semidirect |
| 7. #11926686 | C2 | semidirect |
| 8. #11926676 | C2 | semidirect |
| 9. C4×#64516 | C2 | semidirect |
| 10. #11926623 | C2 | semidirect |
| 11. C19×#493 | C2 | semidirect |
| 12. C2×#64543 | C22 | semidirect |
| 15. C2×D8×C19 | C22 | semidirect |
| 16. C2×D8×C19 | C22 | semidirect |
| 18. C19×#127 | C22 | semidirect |
| 23. #10597384 | C22 | semidirect |
| 26. C2×#64526 | C22 | semidirect |
| 30. C2×#64515 | C22 | semidirect |
| 33. C4×Dic38 | C22 | semidirect |
| 34. C4×C8×C19 | C22 | semidirect |
| 35. #10597289 | C22 | semidirect |
| 36. #10597289 | C22 | semidirect |
| 38. (C2×D19)⋊C8 | C22 | semidirect |
| 39. #10597274 | C22 | semidirect |
| 40. #10597273 | C22 | semidirect |
| 41. C4⋊(C19⋊C8) | C22 | semidirect |
| 81. #64516 | D4 | semidirect |
| 117. Dic38 | C2×D4 | semidirect |
| 119. C8×C19 | C2×D4 | semidirect |
| 137. C4×C19 | AGL(1,ℤ/8) | semidirect |
| 147. #493 | D19 | semidirect |
| 169. C2×D8 | C2×D19 | semidirect |
| 170. C2×D8 | C2×D19 | semidirect |
| 174. #127 | C2×D19 | semidirect |
| 191. C4×C8 | C2×D19 | semidirect |
| 192. C19 | #3274 | semidirect |
| 271. C8 | D4×D19 | semidirect |
| 291. C4 | #10597357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597357 | 2 |
| #11927214 | 2 |
| #11927179 | 2 |
| #11926794 | 2 |
| #11926741 | 2 |
| #11926736 | 2 |
| #11926686 | 2 |
| #11926676 | 2 |
| C4×#64516 | 2 |
| #11926623 | 2 |
| C19×#493 | 2 |
| #3274 | 19 |