Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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. C2×#22575476 | C2 | semidirect |
| 2. C2×D8×D269 | C2 | semidirect |
| 3. #31771248 | C2 | semidirect |
| 4. #31770843 | C2 | semidirect |
| 5. #31770838 | C2 | semidirect |
| 6. #31770817 | C2 | semidirect |
| 7. #31770754 | C2 | semidirect |
| 8. #31770749 | C2 | semidirect |
| 9. C4×D2152 | C2 | semidirect |
| 10. C8×D1076 | C2 | semidirect |
| 11. #495×C269 | C2 | semidirect |
| 12. C2×#16864403 | C22 | semidirect |
| 15. C2×#16864389 | C22 | semidirect |
| 20. C2×C8×D269 | C22 | semidirect |
| 24. #22575424 | C22 | semidirect |
| 27. C4×D1076 | C22 | semidirect |
| 29. #22575387 | C22 | semidirect |
| 30. C4⋊#14524130 | C22 | semidirect |
| 31. #22575377 | C22 | semidirect |
| 32. #22575375 | C22 | semidirect |
| 33. #22575374 | C22 | semidirect |
| 35. #22575365 | C22 | semidirect |
| 36. C2×Q16×C269 | C22 | semidirect |
| 37. C2×SD16×C269 | C22 | semidirect |
| 39. #124×C269 | C22 | semidirect |
| 40. C4×C8×C269 | C22 | semidirect |
| 56. D2152 | D4 | semidirect |
| 127. C2×D269 | #135 | semidirect |
| 143. C269 | #3280 | semidirect |
| 148. #495 | D269 | semidirect |
| 159. C2×Q16 | C2×D269 | semidirect |
| 161. C2×SD16 | C2×D269 | semidirect |
| 168. #124 | C2×D269 | semidirect |
| 184. C4×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575476 | 2 |
| C2×D8×D269 | 2 |
| #31771248 | 2 |
| #31770843 | 2 |
| #31770838 | 2 |
| #31770817 | 2 |
| #31770754 | 2 |
| #31770749 | 2 |
| C4×D2152 | 2 |
| C8×D1076 | 2 |
| #495×C269 | 2 |
| #3280 | 269 |