Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 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. #11927347 | C2 | semidirect |
| 2. #11927346 | C2 | semidirect |
| 3. #11926919 | C2 | semidirect |
| 4. #11926814 | C2 | semidirect |
| 5. #11926812 | C2 | semidirect |
| 6. #11926811 | C2 | semidirect |
| 7. #11926712 | C2 | semidirect |
| 8. #11926710 | C2 | semidirect |
| 9. #11926661 | C2 | semidirect |
| 10. #11926659 | C2 | semidirect |
| 11. C19×#576 | C2 | semidirect |
| 12. C19×H(5,𝔽2) | C22 | semidirect |
| 13. #10597435 | C22 | semidirect |
| 15. C19×AGL(1,ℤ/8) | C22 | semidirect |
| 19. C2×D8×C19 | C22 | semidirect |
| 20. C19×#131 | C22 | semidirect |
| 24. #10597395 | C22 | semidirect |
| 25. #10597395 | C22 | semidirect |
| 26. #10597394 | C22 | semidirect |
| 27. #10597386 | C22 | semidirect |
| 29. #10597378 | C22 | semidirect |
| 31. C2×#64525 | C22 | semidirect |
| 35. C2×D152 | C22 | semidirect |
| 36. #10597347 | C22 | semidirect |
| 37. #10597294 | C22 | semidirect |
| 38. #10597294 | C22 | semidirect |
| 39. #10597290 | C22 | semidirect |
| 40. #10597282 | C22 | semidirect |
| 41. #10597280 | C22 | semidirect |
| 42. #10597279 | C22 | semidirect |
| 43. #10597276 | C22 | semidirect |
| 44. C8×Dic19 | C22 | semidirect |
| 61. Q16×C19 | D4 | semidirect |
| 63. SD16×C19 | D4 | semidirect |
| 67. D8×C19 | D4 | semidirect |
| 72. #64528 | D4 | semidirect |
| 75. #64527 | D4 | semidirect |
| 77. #64526 | D4 | semidirect |
| 83. #64525 | D4 | semidirect |
| 149. #576 | D19 | semidirect |
| 166. H(5,𝔽2) | C2×D19 | semidirect |
| 174. AGL(1,ℤ/8) | C2×D19 | semidirect |
| 185. C2×D8 | C2×D19 | semidirect |
| 188. #131 | C2×D19 | semidirect |
| 198. C19 | #3292 | semidirect |
| 216. Q16 | C22⋊D19 | semidirect |
| 223. SD16 | C22⋊D19 | semidirect |
| 235. D8 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927347 | 2 |
| #11927346 | 2 |
| #11926919 | 2 |
| #11926814 | 2 |
| #11926812 | 2 |
| #11926811 | 2 |
| #11926712 | 2 |
| #11926710 | 2 |
| #11926661 | 2 |
| #11926659 | 2 |
| C19×#576 | 2 |
| #3292 | 19 |