Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597358 | C2 | semidirect |
| 2. #11927188 | C2 | semidirect |
| 3. #11926927 | C2 | semidirect |
| 4. #11926785 | C2 | semidirect |
| 5. #11926777 | C2 | semidirect |
| 6. #11926757 | C2 | semidirect |
| 7. #11926695 | C2 | semidirect |
| 8. #11926686 | C2 | semidirect |
| 9. D8×Dic19 | C2 | semidirect |
| 10. C8×C22⋊D19 | C2 | semidirect |
| 11. C22×D8×C19 | C2 | semidirect |
| 13. C2×#64543 | C22 | semidirect |
| 22. #10597384 | C22 | semidirect |
| 23. #10597382 | C22 | semidirect |
| 25. D4×Dic19 | C22 | semidirect |
| 26. C2×#64526 | C22 | semidirect |
| 27. C2×#64526 | C22 | semidirect |
| 31. C2×Dic76 | C22 | semidirect |
| 32. C2×C8×D19 | C22 | semidirect |
| 33. #10597289 | C22 | semidirect |
| 34. #10597289 | C22 | semidirect |
| 36. (C2×D19)⋊C8 | C22 | semidirect |
| 37. #10597275 | C22 | semidirect |
| 38. #10597273 | C22 | semidirect |
| 39. Dic19⋊C8 | C22 | semidirect |
| 40. C8×Dic19 | C22 | semidirect |
| 59. D8×C19 | D4 | semidirect |
| 124. C22×C19 | #135 | semidirect |
| 138. C22×D8 | D19 | semidirect |
| 184. C19 | #3280 | semidirect |
| 206. D8 | C22⋊D19 | semidirect |
| 270. C22 | #10597358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597358 | 2 |
| #11927188 | 2 |
| #11926927 | 2 |
| #11926785 | 2 |
| #11926777 | 2 |
| #11926757 | 2 |
| #11926695 | 2 |
| #11926686 | 2 |
| D8×Dic19 | 2 |
| C8×C22⋊D19 | 2 |
| C22×D8×C19 | 2 |
| #3280 | 19 |