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. #31771088 | C2 | semidirect |
| 3. #31770611 | C2 | semidirect |
| 4. #31770607 | C2 | semidirect |
| 5. #31770602 | C2 | semidirect |
| 6. C2×#22575375 | C2 | semidirect |
| 7. C2×#131×C269 | C2 | semidirect |
| 9. #22575499 | C4 | semidirect |
| 16. #22575412 | C22 | semidirect |
| 17. C2×C4⋊Dic269 | C22 | semidirect |
| 18. #22575378 | C22 | semidirect |
| 19. #22575378 | C22 | semidirect |
| 20. #22575375 | C22 | semidirect |
| 21. #22575375 | C22 | semidirect |
| 22. #22575375 | C22 | semidirect |
| 25. C2×M16×C269 | C22 | semidirect |
| 26. C22×C8×C269 | C22 | semidirect |
| 30. #16864402 | C2×C4 | semidirect |
| 34. C2×D1076 | C2×C4 | semidirect |
| 97. C269 | #2897 | semidirect |
| 100. C2×#131 | D269 | semidirect |
| 114. C2×M16 | C2×D269 | semidirect |
| 115. C22×C8 | 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 |
| #31771088 | 2 |
| #31770611 | 2 |
| #31770607 | 2 |
| #31770602 | 2 |
| C2×#22575375 | 2 |
| C2×#131×C269 | 2 |
| #2897 | 269 |