Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×#22575460 | C2 | semidirect |
| 3. #31770609 | C2 | semidirect |
| 4. #31770604 | C2 | semidirect |
| 5. #31770599 | C2 | semidirect |
| 6. C2×#22575373 | C2 | semidirect |
| 7. #520×C269 | C2 | semidirect |
| 9. #22575499 | C4 | semidirect |
| 15. C2×#16864386 | C22 | semidirect |
| 16. C22×#14524130 | C22 | semidirect |
| 17. #22575376 | C22 | semidirect |
| 18. #22575376 | C22 | semidirect |
| 19. #22575373 | C22 | semidirect |
| 20. #22575373 | C22 | semidirect |
| 21. #22575373 | C22 | semidirect |
| 25. #117×C269 | C22 | semidirect |
| 26. C2×C4⋊C4×C269 | C22 | semidirect |
| 30. #16864402 | C2×C4 | semidirect |
| 34. C2×D1076 | C2×C4 | semidirect |
| 97. C269 | #2897 | semidirect |
| 101. #520 | D269 | semidirect |
| 118. #117 | C2×D269 | semidirect |
| 119. C2×C4⋊C4 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575499 | 2 |
| C2×#22575460 | 2 |
| #31770609 | 2 |
| #31770604 | 2 |
| #31770599 | 2 |
| C2×#22575373 | 2 |
| #520×C269 | 2 |
| #2897 | 269 |