Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 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. #31774442 | C2 | semidirect |
| 2. C2×#22576122 | C2 | semidirect |
| 3. #31774210 | C2 | semidirect |
| 4. #31774176 | C2 | semidirect |
| 5. #31774091 | C2 | semidirect |
| 6. #31774033 | C2 | semidirect |
| 7. #31774030 | C2 | semidirect |
| 8. #31773979 | C2 | semidirect |
| 9. #31773977 | C2 | semidirect |
| 10. #31773947 | C2 | semidirect |
| 11. #480×C271 | C2 | semidirect |
| 17. #22576159 | C22 | semidirect |
| 18. #22576156 | C22 | semidirect |
| 22. D4×Dic271 | C22 | semidirect |
| 27. #22576122 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 35. #22576080 | C22 | semidirect |
| 37. C8×Dic271 | C22 | semidirect |
| 40. #107×C271 | C22 | semidirect |
| 41. #102×C271 | C22 | semidirect |
| 92. D1084 | #41 | semidirect |
| 99. C2×Dic271 | D8 | semidirect |
| 149. C271 | #3100 | semidirect |
| 154. #480 | D271 | semidirect |
| 184. #107 | C2×D271 | semidirect |
| 189. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774442 | 2 |
| C2×#22576122 | 2 |
| #31774210 | 2 |
| #31774176 | 2 |
| #31774091 | 2 |
| #31774033 | 2 |
| #31774030 | 2 |
| #31773979 | 2 |
| #31773977 | 2 |
| #31773947 | 2 |
| #480×C271 | 2 |
| #3100 | 271 |