Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597354 | C2 | semidirect |
| 2. C2×#10597396 | C2 | semidirect |
| 3. C22×#64525 | C2 | semidirect |
| 4. #11927111 | C2 | semidirect |
| 5. #11927108 | C2 | semidirect |
| 6. #11926932 | C2 | semidirect |
| 7. #11926930 | C2 | semidirect |
| 8. #11926925 | C2 | semidirect |
| 9. #11926919 | C2 | semidirect |
| 10. #11926502 | C2 | semidirect |
| 11. C2×C19×AGL(1,ℤ/8) | C2 | semidirect |
| 17. C2×SD16×C19 | C22 | semidirect |
| 18. C2×D8×C19 | C22 | semidirect |
| 22. #10597393 | C22 | semidirect |
| 23. C2×#64528 | C22 | semidirect |
| 24. C2×#64527 | C22 | semidirect |
| 25. #10597386 | C22 | semidirect |
| 26. #10597386 | C22 | semidirect |
| 29. #10597382 | C22 | semidirect |
| 30. C2×#64526 | C22 | semidirect |
| 34. C2×#64525 | C22 | semidirect |
| 39. C2×D152 | C22 | semidirect |
| 40. C2×#64516 | C22 | semidirect |
| 41. #10597272 | C22 | semidirect |
| 42. C8×Dic19 | C22 | semidirect |
| 70. M16×C19 | D4 | semidirect |
| 83. C2×C19⋊C8 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D19 | semidirect |
| 176. C2×SD16 | C2×D19 | semidirect |
| 182. C2×D8 | C2×D19 | semidirect |
| 196. C19 | #3155 | semidirect |
| 232. M16 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597354 | 2 |
| C2×#10597396 | 2 |
| C22×#64525 | 2 |
| #11927111 | 2 |
| #11927108 | 2 |
| #11926932 | 2 |
| #11926930 | 2 |
| #11926925 | 2 |
| #11926919 | 2 |
| #11926502 | 2 |
| C2×C19×AGL(1,ℤ/8) | 2 |
| #3155 | 19 |