Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #31773797 | C2 | semidirect |
| 3. #31773788 | C2 | semidirect |
| 4. #31773787 | C2 | semidirect |
| 5. #31773785 | C2 | semidirect |
| 6. #31773777 | C2 | semidirect |
| 7. #31773774 | C2 | semidirect |
| 8. #31773752 | C2 | semidirect |
| 9. #390×C271 | C2 | semidirect |
| 12. C23×Dic271 | C22 | semidirect |
| 13. #22576128 | C4 | semidirect |
| 14. C2×Dic271⋊C4 | C22 | semidirect |
| 17. C2×C22⋊Dic271 | C22 | semidirect |
| 23. C2×C4×Dic271 | C22 | semidirect |
| 24. C271⋊#95 | C22 | semidirect |
| 25. C271⋊#95 | C22 | semidirect |
| 26. C271⋊#95 | C22 | semidirect |
| 28. C2×C4⋊C4×C271 | C22 | semidirect |
| 30. C2×C22⋊C4×C271 | C22 | semidirect |
| 31. C2×C42×C271 | C22 | semidirect |
| 36. C23×D271 | C2×C4 | semidirect |
| 49. C22⋊Dic271 | C2×C4 | semidirect |
| 54. (C2×D271)⋊C4 | C2×C4 | semidirect |
| 149. C271 | #2375 | semidirect |
| 153. #390 | D271 | semidirect |
| 166. C2×C4⋊C4 | C2×D271 | semidirect |
| 176. C2×C22⋊C4 | C2×D271 | semidirect |
| 178. C2×C42 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576128 | 2 |
| #31773797 | 2 |
| #31773788 | 2 |
| #31773787 | 2 |
| #31773785 | 2 |
| #31773777 | 2 |
| #31773774 | 2 |
| #31773752 | 2 |
| #390×C271 | 2 |
| #2375 | 271 |