Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #31771160 | C2 | semidirect |
| 3. #31770968 | C2 | semidirect |
| 4. #31770953 | C2 | semidirect |
| 5. #31770952 | C2 | semidirect |
| 6. #31770951 | C2 | semidirect |
| 7. #31770608 | C2 | semidirect |
| 8. C4×#16864385 | C2 | semidirect |
| 9. #486×C269 | C2 | semidirect |
| 14. #22575453 | C22 | semidirect |
| 19. #22575444 | C22 | semidirect |
| 26. #22575375 | C22 | semidirect |
| 27. #22575374 | C22 | semidirect |
| 28. #22575373 | C22 | semidirect |
| 29. #22575363 | C22 | semidirect |
| 30. C4×#14524130 | C22 | semidirect |
| 31. C4⋊Q8×C269 | C22 | semidirect |
| 33. #102×C269 | C22 | semidirect |
| 34. C4×C8×C269 | C22 | semidirect |
| 123. C269 | #3138 | semidirect |
| 131. #486 | D269 | semidirect |
| 139. C4⋊Q8 | C2×D269 | semidirect |
| 155. #102 | C2×D269 | semidirect |
| 158. C4×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771160 | 2 |
| #127×D269 | 2 |
| #31770968 | 2 |
| #31770953 | 2 |
| #31770952 | 2 |
| #31770951 | 2 |
| #31770608 | 2 |
| C4×#16864385 | 2 |
| #486×C269 | 2 |
| #3138 | 269 |