Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
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. #31774245 | C2 | semidirect |
| 3. #31774215 | C2 | semidirect |
| 4. #31774184 | C2 | semidirect |
| 5. #31774128 | C2 | semidirect |
| 6. #31774097 | C2 | semidirect |
| 7. #31774047 | C2 | semidirect |
| 8. C4×#16864641 | C2 | semidirect |
| 9. D4×C271⋊C8 | C2 | semidirect |
| 10. C2×#22576080 | C2 | semidirect |
| 11. #554×C271 | C2 | semidirect |
| 15. C2×#16864641 | C22 | semidirect |
| 16. C22×C271⋊C8 | C22 | semidirect |
| 22. #22576091 | C22 | semidirect |
| 23. #22576091 | C22 | semidirect |
| 24. C4⋊(C271⋊C8) | C22 | semidirect |
| 25. #22576084 | C22 | semidirect |
| 28. #22576080 | C22 | semidirect |
| 29. #22576080 | C22 | semidirect |
| 30. #22576080 | C22 | semidirect |
| 31. C22⋊(C271⋊C8) | C22 | semidirect |
| 32. C4×C271⋊C8 | C22 | semidirect |
| 33. C4⋊Q8×C271 | C22 | semidirect |
| 36. C22⋊Q8×C271 | C22 | semidirect |
| 37. C4×Q8×C271 | C22 | semidirect |
| 40. C2×C4⋊C4×C271 | C22 | semidirect |
| 99. D4×C271 | SD16 | semidirect |
| 136. C271 | #3295 | semidirect |
| 138. #554 | D271 | semidirect |
| 154. C4⋊Q8 | C2×D271 | semidirect |
| 158. C22⋊Q8 | C2×D271 | semidirect |
| 162. C4×Q8 | C2×D271 | semidirect |
| 166. C2×C4⋊C4 | C2×D271 | semidirect |
| 231. D4 | #16864641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D1084 | 2 |
| #31774245 | 2 |
| #31774215 | 2 |
| #31774184 | 2 |
| #31774128 | 2 |
| #31774097 | 2 |
| #31774047 | 2 |
| C4×#16864641 | 2 |
| D4×C271⋊C8 | 2 |
| C2×#22576080 | 2 |
| #554×C271 | 2 |
| #3295 | 271 |