Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11927352 | C2 | semidirect |
| 2. #11927346 | C2 | semidirect |
| 3. #11926929 | C2 | semidirect |
| 4. #11926816 | C2 | semidirect |
| 5. #11926814 | C2 | semidirect |
| 6. #11926809 | C2 | semidirect |
| 7. #11926720 | C2 | semidirect |
| 8. #11926717 | C2 | semidirect |
| 9. #11926661 | C2 | semidirect |
| 10. #11926659 | C2 | semidirect |
| 11. C19×#578 | C2 | semidirect |
| 12. C19×2−1+4 | C22 | semidirect |
| 15. C19×#137 | C22 | semidirect |
| 19. C2×Q16×C19 | C22 | semidirect |
| 20. C19×#131 | C22 | semidirect |
| 25. #10597395 | C22 | semidirect |
| 26. #10597394 | C22 | semidirect |
| 27. #10597393 | C22 | semidirect |
| 31. C2×#64527 | C22 | semidirect |
| 37. #10597294 | C22 | semidirect |
| 38. #10597294 | C22 | semidirect |
| 39. #10597293 | C22 | semidirect |
| 41. #10597280 | C22 | semidirect |
| 42. #10597279 | C22 | semidirect |
| 43. #10597276 | C22 | semidirect |
| 44. C8×Dic19 | C22 | semidirect |
| 144. #578 | D19 | semidirect |
| 161. 2−1+4 | C2×D19 | semidirect |
| 166. #137 | C2×D19 | semidirect |
| 177. C2×Q16 | C2×D19 | semidirect |
| 184. #131 | C2×D19 | semidirect |
| 194. C19 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927352 | 2 |
| #11927346 | 2 |
| #11926929 | 2 |
| #11926816 | 2 |
| #11926814 | 2 |
| #11926809 | 2 |
| #11926720 | 2 |
| #11926717 | 2 |
| #11926661 | 2 |
| #11926659 | 2 |
| C19×#578 | 2 |
| #3290 | 19 |