Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
468 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 121 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. C22⋊Q8×D19 | C2 | semidirect |
| 3. #11926874 | C2 | semidirect |
| 4. #11926864 | C2 | semidirect |
| 5. #11926776 | C2 | semidirect |
| 6. #11926774 | C2 | semidirect |
| 7. #11926697 | C2 | semidirect |
| 8. #11926694 | C2 | semidirect |
| 9. #11926684 | C2 | semidirect |
| 10. C22⋊C8×D19 | C2 | semidirect |
| 11. C19×#483 | C2 | semidirect |
| 12. C2×Q8×D19 | C22 | semidirect |
| 18. #10597392 | C22 | semidirect |
| 19. C2×#64527 | C22 | semidirect |
| 22. C2×#64516 | C22 | semidirect |
| 23. C2×C8×D19 | C22 | semidirect |
| 24. #10597343 | C22 | semidirect |
| 31. C4⋊C4×D19 | C22 | semidirect |
| 34. C19×#106 | C22 | semidirect |
| 35. C19×#103 | C22 | semidirect |
| 38. #10597278 | C22 | semidirect |
| 39. (C2×D19)⋊C8 | C22 | semidirect |
| 40. #10597267 | C22 | semidirect |
| 41. #10597266 | C22 | semidirect |
| 42. #10597265 | C22 | semidirect |
| 92. C22×D19 | SD16 | semidirect |
| 151. #483 | D19 | semidirect |
| 189. #106 | C2×D19 | semidirect |
| 191. #103 | C2×D19 | semidirect |
| 197. C19 | #3187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊Q8×D19 | 2 |
| C2×#10597341 | 2 |
| #11926874 | 2 |
| #11926864 | 2 |
| #11926776 | 2 |
| #11926774 | 2 |
| #11926697 | 2 |
| #11926694 | 2 |
| #11926684 | 2 |
| C22⋊C8×D19 | 2 |
| C19×#483 | 2 |
| #3187 | 19 |