Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #31771371 | C2 | semidirect |
| 3. #31770728 | C2 | semidirect |
| 4. #31770723 | C2 | semidirect |
| 5. #31770654 | C2 | semidirect |
| 6. C2×#22575381 | C2 | semidirect |
| 7. C4×M16×C269 | C2 | semidirect |
| 9. #22575486 | C4 | semidirect |
| 10. #22575481 | C4 | semidirect |
| 13. #22575459 | C22 | semidirect |
| 16. #22575389 | C22 | semidirect |
| 17. #22575381 | C22 | semidirect |
| 18. #22575381 | C22 | semidirect |
| 22. #97×C269 | C22 | semidirect |
| 23. C4×C8×C269 | C22 | semidirect |
| 32. Dic1076 | C2×C4 | semidirect |
| 33. #16864391 | C2×C4 | semidirect |
| 34. D2152 | C2×C4 | semidirect |
| 85. C269 | #2956 | semidirect |
| 93. C4×M16 | D269 | semidirect |
| 108. #97 | C2×D269 | semidirect |
| 109. C4×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771405 | 2 |
| #31771371 | 2 |
| #31770728 | 2 |
| #31770723 | 2 |
| #31770654 | 2 |
| C2×#22575381 | 2 |
| C4×M16×C269 | 2 |
| #2956 | 269 |