Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22575480 | C2 | semidirect |
| 2. #31771156 | C2 | semidirect |
| 3. #127×D269 | C2 | semidirect |
| 4. #31770991 | C2 | semidirect |
| 5. #31770982 | C2 | semidirect |
| 6. #31770981 | C2 | semidirect |
| 7. #31770979 | C2 | semidirect |
| 8. C4×#16864385 | C2 | semidirect |
| 9. #492×C269 | C2 | semidirect |
| 14. C2×#16864389 | C22 | semidirect |
| 15. C2×D2152 | C22 | semidirect |
| 16. C2×#16864387 | C22 | semidirect |
| 19. #22575450 | C22 | semidirect |
| 22. #22575442 | C22 | semidirect |
| 26. #22575363 | C22 | semidirect |
| 27. C4×#14524130 | C22 | semidirect |
| 28. C2×SD16×C269 | C22 | semidirect |
| 29. C4⋊Q8×C269 | C22 | semidirect |
| 31. C4×C8×C269 | C22 | semidirect |
| 49. #16864385 | D4 | semidirect |
| 78. #14524130 | C2×D4 | semidirect |
| 86. C8×C269 | C2×D4 | semidirect |
| 98. C4×C269 | AGL(1,ℤ/8) | semidirect |
| 108. C269 | #3151 | semidirect |
| 117. #492 | D269 | semidirect |
| 124. C2×SD16 | C2×D269 | semidirect |
| 128. C4⋊Q8 | C2×D269 | semidirect |
| 140. C4×C8 | C2×D269 | semidirect |
| 195. C8 | D4×D269 | semidirect |
| 209. C4 | #22575480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575480 | 2 |
| #31771156 | 2 |
| #127×D269 | 2 |
| #31770991 | 2 |
| #31770982 | 2 |
| #31770981 | 2 |
| #31770979 | 2 |
| C4×#16864385 | 2 |
| #492×C269 | 2 |
| #3151 | 269 |