Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×D1076 | C2 | semidirect |
| 2. #31770921 | C2 | semidirect |
| 3. #31770892 | C2 | semidirect |
| 4. #31770797 | C2 | semidirect |
| 5. #31770738 | C2 | semidirect |
| 6. #31770715 | C2 | semidirect |
| 7. #31770662 | C2 | semidirect |
| 8. #532×C269 | C2 | semidirect |
| 18. #22575384 | C22 | semidirect |
| 19. C4⋊#14524130 | C22 | semidirect |
| 20. #22575374 | C22 | semidirect |
| 23. #22575364 | C22 | semidirect |
| 25. C4⋊Q8×C269 | C22 | semidirect |
| 26. #127×C269 | C22 | semidirect |
| 31. C4×D4×C269 | C22 | semidirect |
| 71. D1076 | #41 | semidirect |
| 120. C269 | #3109 | semidirect |
| 122. #532 | D269 | semidirect |
| 134. C4⋊Q8 | C2×D269 | semidirect |
| 135. #127 | C2×D269 | semidirect |
| 144. C4×D4 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1076 | 2 |
| #31770921 | 2 |
| #31770892 | 2 |
| #31770797 | 2 |
| #31770738 | 2 |
| #31770715 | 2 |
| #31770662 | 2 |
| #532×C269 | 2 |
| #3109 | 269 |