Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774714 | C2 | semidirect |
| 2. #31774707 | C2 | semidirect |
| 3. #31774698 | C2 | semidirect |
| 4. #31774280 | C2 | semidirect |
| 5. #31774173 | C2 | semidirect |
| 6. #31774159 | C2 | semidirect |
| 7. #31774077 | C2 | semidirect |
| 8. #31774068 | C2 | semidirect |
| 9. #31774013 | C2 | semidirect |
| 10. #31774012 | C2 | semidirect |
| 11. #472×C271 | C2 | semidirect |
| 12. #22576207 | C22 | semidirect |
| 16. #22576193 | C22 | semidirect |
| 27. C2×Dic1084 | C22 | semidirect |
| 28. C2×#16864642 | C22 | semidirect |
| 31. #22576168 | C22 | semidirect |
| 33. #22576147 | C22 | semidirect |
| 34. #22576095 | C22 | semidirect |
| 35. #22576087 | C22 | semidirect |
| 37. #22576086 | C22 | semidirect |
| 38. #22576078 | C22 | semidirect |
| 39. C8×Dic271 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C271 | C22 | semidirect |
| 42. #131×C271 | C22 | semidirect |
| 43. #108×C271 | C22 | semidirect |
| 44. #100×C271 | C22 | semidirect |
| 149. C271 | #3290 | semidirect |
| 156. #472 | D271 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D271 | semidirect |
| 185. #131 | C2×D271 | semidirect |
| 188. #108 | C2×D271 | semidirect |
| 193. #100 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774714 | 2 |
| #31774707 | 2 |
| #31774698 | 2 |
| #31774280 | 2 |
| #31774173 | 2 |
| #31774159 | 2 |
| #31774077 | 2 |
| #31774068 | 2 |
| #31774013 | 2 |
| #31774012 | 2 |
| #472×C271 | 2 |
| #3290 | 271 |