Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
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. #31771419 | C2 | semidirect |
| 2. #31771417 | C2 | semidirect |
| 3. #31771407 | C2 | semidirect |
| 4. #31770989 | C2 | semidirect |
| 5. #31770881 | C2 | semidirect |
| 6. #31770876 | C2 | semidirect |
| 7. #31770868 | C2 | semidirect |
| 8. #31770784 | C2 | semidirect |
| 9. #31770779 | C2 | semidirect |
| 10. #31770723 | C2 | semidirect |
| 11. #443×C269 | C2 | semidirect |
| 12. #22575500 | C22 | semidirect |
| 16. #22575483 | C22 | semidirect |
| 19. #22575481 | C22 | semidirect |
| 26. C2×Dic1076 | C22 | semidirect |
| 29. C2×#16864391 | C22 | semidirect |
| 33. #22575459 | C22 | semidirect |
| 34. #22575441 | C22 | semidirect |
| 35. #22575389 | C22 | semidirect |
| 37. #22575381 | C22 | semidirect |
| 38. #22575371 | C22 | semidirect |
| 39. #22575369 | C22 | semidirect |
| 41. #131×C269 | C22 | semidirect |
| 42. #108×C269 | C22 | semidirect |
| 43. #104×C269 | C22 | semidirect |
| 44. C4×C8×C269 | C22 | semidirect |
| 149. C269 | #3290 | semidirect |
| 161. #443 | D269 | semidirect |
| 185. #131 | C2×D269 | semidirect |
| 188. #108 | C2×D269 | semidirect |
| 191. #104 | C2×D269 | semidirect |
| 194. C4×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771419 | 2 |
| #31771417 | 2 |
| #31771407 | 2 |
| #31770989 | 2 |
| #31770881 | 2 |
| #31770876 | 2 |
| #31770868 | 2 |
| #31770784 | 2 |
| #31770779 | 2 |
| #31770723 | 2 |
| #443×C269 | 2 |
| #3290 | 269 |