Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #31770943 | C2 | semidirect |
| 3. #31770902 | C2 | semidirect |
| 4. #31770807 | C2 | semidirect |
| 6. #31770703 | C2 | semidirect |
| 7. C4×#16864389 | C2 | semidirect |
| 8. #31770666 | C2 | semidirect |
| 9. #541×C269 | C2 | semidirect |
| 18. #22575386 | C22 | semidirect |
| 19. #22575384 | C22 | semidirect |
| 20. C4⋊#14524130 | C22 | semidirect |
| 21. #22575377 | C22 | semidirect |
| 22. #22575377 | C22 | semidirect |
| 26. #22575364 | C22 | semidirect |
| 27. C4×#14524130 | C22 | semidirect |
| 28. C4⋊Q8×C269 | C22 | semidirect |
| 31. #125×C269 | C22 | semidirect |
| 33. C4×Q8×C269 | C22 | semidirect |
| 102. C269 | #3123 | semidirect |
| 104. #541 | D269 | semidirect |
| 116. C4⋊Q8 | C2×D269 | semidirect |
| 119. #125 | C2×D269 | semidirect |
| 121. C4×Q8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771079 | 2 |
| #31770943 | 2 |
| #31770902 | 2 |
| #31770807 | 2 |
| #31770755 | 2 |
| #31770703 | 2 |
| C4×#16864389 | 2 |
| #31770666 | 2 |
| #541×C269 | 2 |
| #3123 | 269 |