Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #31771150 | C2 | semidirect |
| 2. C2×D4×Dic269 | C2 | semidirect |
| 3. #31770924 | C2 | semidirect |
| 4. #31770921 | C2 | semidirect |
| 5. #31770893 | C2 | semidirect |
| 6. #31770798 | C2 | semidirect |
| 7. #31770739 | C2 | semidirect |
| 8. #31770717 | C2 | semidirect |
| 9. #31770714 | C2 | semidirect |
| 10. #31770659 | C2 | semidirect |
| 11. #447×C269 | C2 | semidirect |
| 15. #22575452 | C22 | semidirect |
| 16. #22575449 | C22 | semidirect |
| 24. D4×Dic269 | C22 | semidirect |
| 25. #22575415 | C22 | semidirect |
| 30. #22575385 | C22 | semidirect |
| 31. #22575384 | C22 | semidirect |
| 32. #22575382 | C22 | semidirect |
| 33. #22575375 | C22 | semidirect |
| 35. #22575374 | C22 | semidirect |
| 37. #22575363 | C22 | semidirect |
| 113. D4×C269 | #41 | semidirect |
| 149. C269 | #3109 | semidirect |
| 158. #447 | D269 | semidirect |
| 249. D4 | #16864401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771150 | 2 |
| C2×D4×Dic269 | 2 |
| #31770924 | 2 |
| #31770921 | 2 |
| #31770893 | 2 |
| #31770798 | 2 |
| #31770739 | 2 |
| #31770717 | 2 |
| #31770714 | 2 |
| #31770659 | 2 |
| #447×C269 | 2 |
| #3109 | 269 |