Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#10597355 | C2 | semidirect |
| 2. C2×#10597396 | C2 | semidirect |
| 3. C22×#64526 | C2 | semidirect |
| 4. #11927115 | C2 | semidirect |
| 5. #11927111 | C2 | semidirect |
| 6. #11926935 | C2 | semidirect |
| 7. #11926932 | C2 | semidirect |
| 8. #11926927 | C2 | semidirect |
| 9. #11926915 | C2 | semidirect |
| 10. #11926502 | C2 | semidirect |
| 11. C2×C19×AGL(1,ℤ/8) | C2 | semidirect |
| 22. #10597390 | C22 | semidirect |
| 23. C2×#64528 | C22 | semidirect |
| 24. C2×#64527 | C22 | semidirect |
| 28. #10597382 | C22 | semidirect |
| 33. C2×#64526 | C22 | semidirect |
| 34. C2×#64525 | C22 | semidirect |
| 39. C2×Dic76 | C22 | semidirect |
| 40. C2×#64516 | C22 | semidirect |
| 41. #10597272 | C22 | semidirect |
| 42. C8×Dic19 | C22 | semidirect |
| 69. M16×C19 | D4 | semidirect |
| 83. C2×C19⋊C8 | D4 | semidirect |
| 144. C2×AGL(1,ℤ/8) | D19 | semidirect |
| 191. C19 | #3154 | semidirect |
| 226. M16 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597355 | 2 |
| C2×#10597396 | 2 |
| C22×#64526 | 2 |
| #11927115 | 2 |
| #11927111 | 2 |
| #11926935 | 2 |
| #11926932 | 2 |
| #11926927 | 2 |
| #11926915 | 2 |
| #11926502 | 2 |
| C2×C19×AGL(1,ℤ/8) | 2 |
| #3154 | 19 |