Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #31770703 | C2 | semidirect |
| 4. C4×#16864389 | C2 | semidirect |
| 5. #31770641 | C2 | semidirect |
| 6. #31770614 | C2 | semidirect |
| 8. #31770561 | C2 | semidirect |
| 9. #519×C269 | C2 | semidirect |
| 11. C2×#16864389 | C4 | semidirect |
| 20. #22575386 | C22 | semidirect |
| 21. #22575384 | C22 | semidirect |
| 22. #22575377 | C22 | semidirect |
| 24. #22575364 | C22 | semidirect |
| 25. C4×#14524130 | C22 | semidirect |
| 28. C4×Q8×C269 | C22 | semidirect |
| 38. #16864389 | C2×C4 | semidirect |
| 39. #16864389 | C2×C4 | semidirect |
| 41. C2×#14524130 | C2×C4 | semidirect |
| 51. C2×Q8×C269 | C2×C4 | semidirect |
| 103. C269 | #2949 | semidirect |
| 106. #519 | D269 | semidirect |
| 122. C4×Q8 | C2×D269 | semidirect |
| 139. C2×Q8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864389 | 2 |
| #31771079 | 2 |
| #31770703 | 2 |
| C4×#16864389 | 2 |
| #31770641 | 2 |
| #31770614 | 2 |
| #31770609 | 2 |
| #31770561 | 2 |
| #519×C269 | 2 |
| #2949 | 269 |