Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22576180 | C2 | semidirect |
| 2. #31774464 | C2 | semidirect |
| 3. #31774380 | C2 | semidirect |
| 4. #31774117 | C2 | semidirect |
| 5. #31774110 | C2 | semidirect |
| 6. #31774095 | C2 | semidirect |
| 7. #31774090 | C2 | semidirect |
| 8. #31773925 | C2 | semidirect |
| 9. #31773899 | C2 | semidirect |
| 10. C2×#22576081 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C271 | C2 | semidirect |
| 14. C2×#16864644 | C22 | semidirect |
| 15. C2×#16864642 | C22 | semidirect |
| 16. C2×#16864641 | C22 | semidirect |
| 17. C2×#16864639 | C22 | semidirect |
| 24. Q8×Dic271 | C22 | semidirect |
| 26. D4×Dic271 | C22 | semidirect |
| 31. Dic271⋊C8 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 33. #22576085 | C22 | semidirect |
| 34. #22576082 | C22 | semidirect |
| 73. #41×C271 | D4 | semidirect |
| 154. C271 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D271 | semidirect |
| 202. #41 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576180 | 2 |
| #31774464 | 2 |
| #31774380 | 2 |
| #31774117 | 2 |
| #31774110 | 2 |
| #31774095 | 2 |
| #31774090 | 2 |
| #31773925 | 2 |
| #31773899 | 2 |
| C2×#22576081 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3045 | 271 |