Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 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. #31774608 | C2 | semidirect |
| 3. #31774214 | C2 | semidirect |
| 4. #31774184 | C2 | semidirect |
| 5. #31774125 | C2 | semidirect |
| 6. #31774094 | C2 | semidirect |
| 7. #31774049 | C2 | semidirect |
| 8. C4×#16864643 | C2 | semidirect |
| 9. C8×D1084 | C2 | semidirect |
| 10. #102×D271 | C2 | semidirect |
| 11. #486×C271 | C2 | semidirect |
| 15. C2×#16864642 | C22 | semidirect |
| 16. C2×C8×D271 | C22 | semidirect |
| 18. #22576140 | C22 | semidirect |
| 23. C4×Dic542 | C22 | semidirect |
| 27. C4⋊C4×D271 | C22 | semidirect |
| 28. #22576092 | C22 | semidirect |
| 29. #22576091 | C22 | semidirect |
| 30. C4⋊(C271⋊C8) | C22 | semidirect |
| 31. #22576085 | C22 | semidirect |
| 33. #22576081 | C22 | semidirect |
| 35. (C2×D271)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C271 | C22 | semidirect |
| 38. #102×C271 | C22 | semidirect |
| 39. #102×C271 | C22 | semidirect |
| 40. C4×C8×C271 | C22 | semidirect |
| 85. D1084 | SD16 | semidirect |
| 136. C271 | #3295 | semidirect |
| 140. #486 | D271 | semidirect |
| 154. C4⋊Q8 | C2×D271 | semidirect |
| 174. #102 | C2×D271 | semidirect |
| 175. #102 | 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 |
|---|---|
| #31774608 | 2 |
| #31774532 | 2 |
| #31774214 | 2 |
| #31774184 | 2 |
| #31774125 | 2 |
| #31774094 | 2 |
| #31774049 | 2 |
| C4×#16864643 | 2 |
| C8×D1084 | 2 |
| #102×D271 | 2 |
| #486×C271 | 2 |
| #3295 | 271 |