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 |
|---|---|---|
| 2. #31770953 | C2 | semidirect |
| 3. #31770923 | C2 | semidirect |
| 4. #31770892 | C2 | semidirect |
| 5. #31770836 | C2 | semidirect |
| 6. #31770805 | C2 | semidirect |
| 7. #31770755 | C2 | semidirect |
| 8. C4×#16864389 | C2 | semidirect |
| 9. D4×#14524130 | C2 | semidirect |
| 10. C2×#22575373 | C2 | semidirect |
| 11. #554×C269 | C2 | semidirect |
| 15. C2×#16864389 | C22 | semidirect |
| 16. C22×#14524130 | C22 | semidirect |
| 22. #22575384 | C22 | semidirect |
| 23. #22575384 | C22 | semidirect |
| 24. C4⋊#14524130 | C22 | semidirect |
| 25. #22575377 | C22 | semidirect |
| 28. #22575373 | C22 | semidirect |
| 29. #22575373 | C22 | semidirect |
| 30. #22575373 | C22 | semidirect |
| 31. C22⋊#14524130 | C22 | semidirect |
| 32. C4×#14524130 | C22 | semidirect |
| 33. C4⋊Q8×C269 | C22 | semidirect |
| 36. C22⋊Q8×C269 | C22 | semidirect |
| 37. C4×Q8×C269 | C22 | semidirect |
| 40. C2×C4⋊C4×C269 | C22 | semidirect |
| 99. D4×C269 | SD16 | semidirect |
| 136. C269 | #3295 | semidirect |
| 138. #554 | D269 | semidirect |
| 154. C4⋊Q8 | C2×D269 | semidirect |
| 158. C22⋊Q8 | C2×D269 | semidirect |
| 162. C4×Q8 | C2×D269 | semidirect |
| 166. C2×C4⋊C4 | C2×D269 | semidirect |
| 231. D4 | #16864389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D1076 | 2 |
| #31770953 | 2 |
| #31770923 | 2 |
| #31770892 | 2 |
| #31770836 | 2 |
| #31770805 | 2 |
| #31770755 | 2 |
| C4×#16864389 | 2 |
| D4×#14524130 | 2 |
| C2×#22575373 | 2 |
| #554×C269 | 2 |
| #3295 | 269 |