Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D1084 | C2 | semidirect |
| 2. #31774225 | C2 | semidirect |
| 3. #31774208 | C2 | semidirect |
| 4. #31774194 | C2 | semidirect |
| 5. #31774109 | C2 | semidirect |
| 6. #31774047 | C2 | semidirect |
| 8. #31774007 | C2 | semidirect |
| 9. #31773995 | C2 | semidirect |
| 10. #31773954 | C2 | semidirect |
| 11. #529×C271 | C2 | semidirect |
| 22. #22576093 | C22 | semidirect |
| 23. #22576091 | C22 | semidirect |
| 24. C4⋊(C271⋊C8) | C22 | semidirect |
| 25. #22576084 | C22 | semidirect |
| 26. #22576081 | C22 | semidirect |
| 31. #22576071 | C22 | semidirect |
| 33. #125×C271 | C22 | semidirect |
| 34. #124×C271 | C22 | semidirect |
| 38. C4×Q8×C271 | C22 | semidirect |
| 40. C4×D4×C271 | C22 | semidirect |
| 140. C271 | #3114 | semidirect |
| 142. #529 | D271 | semidirect |
| 158. #125 | C2×D271 | semidirect |
| 159. #124 | C2×D271 | semidirect |
| 163. C4×Q8 | C2×D271 | semidirect |
| 169. C4×D4 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1084 | 2 |
| #31774225 | 2 |
| #31774208 | 2 |
| #31774194 | 2 |
| #31774109 | 2 |
| #31774047 | 2 |
| #31774030 | 2 |
| #31774007 | 2 |
| #31773995 | 2 |
| #31773954 | 2 |
| #529×C271 | 2 |
| #3114 | 271 |