Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #31770726 | C2 | semidirect |
| 4. #31770721 | C2 | semidirect |
| 5. C2×#22575379 | C2 | semidirect |
| 6. M16×Dic269 | C2 | semidirect |
| 7. #430×C269 | C2 | semidirect |
| 9. #22575486 | C4 | semidirect |
| 10. #22575481 | C4 | semidirect |
| 12. #22575461 | C22 | semidirect |
| 17. #22575379 | C22 | semidirect |
| 18. #22575379 | C22 | semidirect |
| 19. #22575363 | C22 | semidirect |
| 20. C8×Dic269 | C22 | semidirect |
| 23. #108×C269 | C22 | semidirect |
| 33. Dic1076 | C2×C4 | semidirect |
| 34. #16864391 | C2×C4 | semidirect |
| 35. D2152 | C2×C4 | semidirect |
| 85. C269 | #2956 | semidirect |
| 91. #430 | D269 | semidirect |
| 105. #108 | 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 |
| #31770726 | 2 |
| #31770721 | 2 |
| C2×#22575379 | 2 |
| M16×Dic269 | 2 |
| #430×C269 | 2 |
| #2956 | 269 |