Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11927080 | C2 | semidirect |
| 2. C2×#10597393 | C2 | semidirect |
| 3. #11926929 | C2 | semidirect |
| 4. #11926900 | C2 | semidirect |
| 5. #11926768 | C2 | semidirect |
| 6. #11926762 | C2 | semidirect |
| 7. #11926694 | C2 | semidirect |
| 8. #11926683 | C2 | semidirect |
| 10. #11926594 | C2 | semidirect |
| 11. C19×#451 | C2 | semidirect |
| 14. C2×Q16×C19 | C22 | semidirect |
| 20. #10597393 | C22 | semidirect |
| 21. Q8×Dic19 | C22 | semidirect |
| 23. C2×#64527 | C22 | semidirect |
| 30. #10597339 | C22 | semidirect |
| 32. #10597336 | C22 | semidirect |
| 35. C19×#103 | C22 | semidirect |
| 37. #10597292 | C22 | semidirect |
| 40. Dic19⋊C8 | C22 | semidirect |
| 41. C8×Dic19 | C22 | semidirect |
| 144. #451 | D19 | semidirect |
| 157. C2×Q16 | C2×D19 | semidirect |
| 180. #103 | C2×D19 | semidirect |
| 186. C19 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927080 | 2 |
| C2×#10597393 | 2 |
| #11926929 | 2 |
| #11926900 | 2 |
| #11926768 | 2 |
| #11926762 | 2 |
| #11926694 | 2 |
| #11926683 | 2 |
| #11926680 | 2 |
| #11926594 | 2 |
| C19×#451 | 2 |
| #3211 | 19 |