Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
928 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 209 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. C2×(C22⋊D271)⋊C4 | C2 | semidirect |
| 3. C2×C22⋊C4×D271 | C2 | semidirect |
| 4. #31773785 | C2 | semidirect |
| 5. #31773777 | C2 | semidirect |
| 6. #31773773 | C2 | semidirect |
| 7. #31773768 | C2 | semidirect |
| 8. C4×(C2×D271)⋊C4 | C2 | semidirect |
| 9. #390×C271 | C2 | semidirect |
| 12. C23×Dic271 | C22 | semidirect |
| 15. #22576128 | C4 | semidirect |
| 17. C2×Dic271⋊C4 | C22 | semidirect |
| 20. C2×C22⋊Dic271 | C22 | semidirect |
| 25. C2×C4×Dic271 | C22 | semidirect |
| 26. C271⋊#95 | C22 | semidirect |
| 27. C271⋊#95 | C22 | semidirect |
| 28. C271⋊#95 | C22 | semidirect |
| 30. C2×C4⋊C4×C271 | C22 | semidirect |
| 32. C2×C22⋊C4×C271 | C22 | semidirect |
| 33. C2×C42×C271 | C22 | semidirect |
| 38. C23×D271 | C2×C4 | semidirect |
| 42. C2×C22⋊D271 | C2×C4 | semidirect |
| 57. C22⋊Dic271 | C2×C4 | semidirect |
| 59. (C2×D271)⋊C4 | C2×C4 | semidirect |
| 60. (C2×D271)⋊C4 | D4 | semidirect |
| 66. C2×D4×C271 | C2×C4 | semidirect |
| 142. C2×D271 | C4×D4 | semidirect |
| 157. C271 | #2358 | semidirect |
| 162. #390 | D271 | semidirect |
| 177. C2×C4⋊C4 | C2×D271 | semidirect |
| 186. C2×C22⋊C4 | C2×D271 | semidirect |
| 188. C2×C42 | C2×D271 | semidirect |
| 205. C2×D4 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576128 | 2 |
| C2×(C22⋊D271)⋊C4 | 2 |
| C2×C22⋊C4×D271 | 2 |
| #31773785 | 2 |
| #31773777 | 2 |
| #31773773 | 2 |
| #31773768 | 2 |
| C4×(C2×D271)⋊C4 | 2 |
| #390×C271 | 2 |
| #2358 | 271 |