Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771315 | C2 | semidirect |
| 3. #31770951 | C2 | semidirect |
| 4. #31770922 | C2 | semidirect |
| 5. #31770896 | C2 | semidirect |
| 6. #31770831 | C2 | semidirect |
| 7. #31770754 | C2 | semidirect |
| 8. C4×#16864389 | C2 | semidirect |
| 9. #31770670 | C2 | semidirect |
| 10. #102×D269 | C2 | semidirect |
| 11. #460×C269 | C2 | semidirect |
| 15. C2×C8×D269 | C22 | semidirect |
| 16. #22575453 | C22 | semidirect |
| 19. #22575429 | C22 | semidirect |
| 26. C4⋊C4×D269 | C22 | semidirect |
| 27. #22575385 | C22 | semidirect |
| 28. #22575384 | C22 | semidirect |
| 29. #22575377 | C22 | semidirect |
| 31. #22575374 | C22 | semidirect |
| 32. #22575374 | C22 | semidirect |
| 34. #22575365 | C22 | semidirect |
| 35. C4×#14524130 | C22 | semidirect |
| 36. C2×SD16×C269 | C22 | semidirect |
| 38. C4×Q8×C269 | C22 | semidirect |
| 39. C4⋊C8×C269 | C22 | semidirect |
| 40. #102×C269 | C22 | semidirect |
| 84. D1076 | SD16 | semidirect |
| 136. C269 | #3295 | semidirect |
| 144. #460 | D269 | semidirect |
| 152. C2×SD16 | C2×D269 | semidirect |
| 162. C4×Q8 | C2×D269 | semidirect |
| 169. C4⋊C8 | C2×D269 | semidirect |
| 175. #102 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771315 | 2 |
| #31771240 | 2 |
| #31770951 | 2 |
| #31770922 | 2 |
| #31770896 | 2 |
| #31770831 | 2 |
| #31770754 | 2 |
| C4×#16864389 | 2 |
| #31770670 | 2 |
| #102×D269 | 2 |
| #460×C269 | 2 |
| #3295 | 269 |