Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #31771312 | C2 | semidirect |
| 3. #31770952 | C2 | semidirect |
| 4. #31770924 | C2 | semidirect |
| 5. #31770896 | C2 | semidirect |
| 6. #31770834 | C2 | semidirect |
| 7. #31770806 | C2 | semidirect |
| 8. #31770758 | C2 | semidirect |
| 9. C4×#16864391 | C2 | semidirect |
| 10. C2×#22575375 | C2 | semidirect |
| 11. C8×D4×C269 | C2 | semidirect |
| 15. C2×#16864391 | C22 | semidirect |
| 16. #22575453 | C22 | semidirect |
| 19. #22575432 | C22 | semidirect |
| 24. C4×Dic538 | C22 | semidirect |
| 27. C2×C4⋊Dic269 | C22 | semidirect |
| 28. #22575385 | C22 | semidirect |
| 29. #22575385 | C22 | semidirect |
| 30. #22575378 | C22 | semidirect |
| 33. #22575375 | C22 | semidirect |
| 34. #22575375 | C22 | semidirect |
| 35. #22575375 | C22 | semidirect |
| 36. C22×C8×C269 | C22 | semidirect |
| 38. C4⋊C8×C269 | C22 | semidirect |
| 39. C22⋊C8×C269 | C22 | semidirect |
| 40. C4×C8×C269 | C22 | semidirect |
| 100. D4×C269 | SD16 | semidirect |
| 136. C269 | #3295 | semidirect |
| 147. C8×D4 | D269 | semidirect |
| 153. C22×C8 | C2×D269 | semidirect |
| 169. C4⋊C8 | C2×D269 | semidirect |
| 176. C22⋊C8 | C2×D269 | semidirect |
| 177. C4×C8 | C2×D269 | semidirect |
| 231. D4 | #16864391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771312 | 2 |
| D4×D1076 | 2 |
| #31770952 | 2 |
| #31770924 | 2 |
| #31770896 | 2 |
| #31770834 | 2 |
| #31770806 | 2 |
| #31770758 | 2 |
| C4×#16864391 | 2 |
| C2×#22575375 | 2 |
| C8×D4×C269 | 2 |
| #3295 | 269 |