Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. #31774607 | C2 | semidirect |
| 3. #31774244 | C2 | semidirect |
| 4. #31774217 | C2 | semidirect |
| 5. #31774187 | C2 | semidirect |
| 6. #31774129 | C2 | semidirect |
| 7. #31774097 | C2 | semidirect |
| 8. #31774046 | C2 | semidirect |
| 9. C8×D1084 | C2 | semidirect |
| 10. #102×D271 | C2 | semidirect |
| 11. C4×SD16×C271 | C2 | semidirect |
| 14. C2×#16864641 | C22 | semidirect |
| 15. C2×C8×D271 | C22 | semidirect |
| 16. #22576160 | C22 | semidirect |
| 20. #22576136 | C22 | semidirect |
| 26. C4⋊C4×D271 | C22 | semidirect |
| 27. #22576091 | C22 | semidirect |
| 28. C4⋊(C271⋊C8) | C22 | semidirect |
| 29. #22576082 | C22 | semidirect |
| 30. #22576082 | C22 | semidirect |
| 32. #22576080 | C22 | semidirect |
| 33. (C2×D271)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C271 | C22 | semidirect |
| 37. #106×C271 | C22 | semidirect |
| 38. #103×C271 | C22 | semidirect |
| 40. C4×C8×C271 | C22 | semidirect |
| 88. D1084 | SD16 | semidirect |
| 136. C271 | #3295 | semidirect |
| 146. C4×SD16 | D271 | semidirect |
| 162. C4×Q8 | C2×D271 | semidirect |
| 168. #106 | C2×D271 | semidirect |
| 170. #103 | C2×D271 | semidirect |
| 177. C4×C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774607 | 2 |
| D4×D1084 | 2 |
| #31774244 | 2 |
| #31774217 | 2 |
| #31774187 | 2 |
| #31774129 | 2 |
| #31774097 | 2 |
| #31774046 | 2 |
| C8×D1084 | 2 |
| #102×D271 | 2 |
| C4×SD16×C271 | 2 |
| #3295 | 271 |