Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#22576184 | C2 | semidirect |
| 2. #31774542 | C2 | semidirect |
| 3. #31774281 | C2 | semidirect |
| 4. #31774144 | C2 | semidirect |
| 5. #31774112 | C2 | semidirect |
| 6. #31774060 | C2 | semidirect |
| 7. #31774032 | C2 | semidirect |
| 8. #31773976 | C2 | semidirect |
| 9. C4×D8×C271 | C2 | semidirect |
| 11. C2×D4×D271 | C22 | semidirect |
| 13. C2×Dic1084 | C22 | semidirect |
| 14. C2×#16864643 | C22 | semidirect |
| 15. C2×#16864642 | C22 | semidirect |
| 18. C2×#16864637 | C22 | semidirect |
| 19. #22576148 | C22 | semidirect |
| 21. #22576140 | C22 | semidirect |
| 27. C4⋊(C271⋊C8) | C22 | semidirect |
| 28. #22576083 | C22 | semidirect |
| 29. #22576080 | C22 | semidirect |
| 30. (C2×D271)⋊C8 | C22 | semidirect |
| 32. C4×D4×C271 | C22 | semidirect |
| 33. #107×C271 | C22 | semidirect |
| 34. #102×C271 | C22 | semidirect |
| 35. C4×C8×C271 | C22 | semidirect |
| 65. D8×C271 | D4 | semidirect |
| 124. C271 | #3273 | semidirect |
| 133. C4×D8 | D271 | semidirect |
| 152. C4×D4 | C2×D271 | semidirect |
| 154. #107 | C2×D271 | semidirect |
| 158. #102 | C2×D271 | semidirect |
| 160. C4×C8 | C2×D271 | semidirect |
| 181. D8 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576184 | 2 |
| #31774542 | 2 |
| #31774281 | 2 |
| #31774144 | 2 |
| #31774112 | 2 |
| #31774060 | 2 |
| #31774032 | 2 |
| #31773976 | 2 |
| C4×D8×C271 | 2 |
| #3273 | 271 |