Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. #31771316 | C2 | semidirect |
| 3. #31770953 | C2 | semidirect |
| 4. #31770925 | C2 | semidirect |
| 5. #31770835 | C2 | semidirect |
| 6. #31770806 | C2 | semidirect |
| 7. #31770757 | C2 | semidirect |
| 8. C4×#16864390 | C2 | semidirect |
| 9. #31770670 | C2 | semidirect |
| 10. #102×D269 | C2 | semidirect |
| 11. #476×C269 | C2 | semidirect |
| 14. C2×#16864391 | C22 | semidirect |
| 16. C2×C8×D269 | C22 | semidirect |
| 19. #22575433 | C22 | semidirect |
| 24. C4×Dic538 | C22 | semidirect |
| 27. C4⋊C4×D269 | C22 | semidirect |
| 28. #22575384 | C22 | semidirect |
| 29. #22575376 | C22 | semidirect |
| 30. #22575375 | C22 | semidirect |
| 32. #22575373 | C22 | semidirect |
| 33. #22575373 | C22 | semidirect |
| 34. #22575365 | C22 | semidirect |
| 35. C4×#14524130 | C22 | semidirect |
| 36. C4⋊Q8×C269 | C22 | semidirect |
| 38. #106×C269 | C22 | semidirect |
| 39. C4⋊C8×C269 | C22 | semidirect |
| 89. D1076 | SD16 | semidirect |
| 136. C269 | #3295 | semidirect |
| 142. #476 | D269 | semidirect |
| 154. C4⋊Q8 | C2×D269 | semidirect |
| 168. #106 | C2×D269 | semidirect |
| 169. C4⋊C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771316 | 2 |
| D4×D1076 | 2 |
| #31770953 | 2 |
| #31770925 | 2 |
| #31770835 | 2 |
| #31770806 | 2 |
| #31770757 | 2 |
| C4×#16864390 | 2 |
| #31770670 | 2 |
| #102×D269 | 2 |
| #476×C269 | 2 |
| #3295 | 269 |