Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 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. #31774442 | C2 | semidirect |
| 2. C2×D4×Dic271 | C2 | semidirect |
| 3. #31774211 | C2 | semidirect |
| 4. #31774208 | C2 | semidirect |
| 5. #31774175 | C2 | semidirect |
| 6. #31774090 | C2 | semidirect |
| 7. #31774031 | C2 | semidirect |
| 8. D8×Dic271 | C2 | semidirect |
| 9. #31773977 | C2 | semidirect |
| 10. #31773947 | C2 | semidirect |
| 11. #447×C271 | C2 | semidirect |
| 15. #22576159 | C22 | semidirect |
| 16. #22576156 | C22 | semidirect |
| 24. D4×Dic271 | C22 | semidirect |
| 25. #22576122 | C22 | semidirect |
| 30. #22576094 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 33. #22576082 | C22 | semidirect |
| 35. #22576081 | C22 | semidirect |
| 37. C8×Dic271 | C22 | semidirect |
| 96. C2×Dic271 | D8 | semidirect |
| 113. D4×C271 | #41 | semidirect |
| 149. C271 | #3100 | semidirect |
| 158. #447 | D271 | semidirect |
| 249. D4 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774442 | 2 |
| C2×D4×Dic271 | 2 |
| #31774211 | 2 |
| #31774208 | 2 |
| #31774175 | 2 |
| #31774090 | 2 |
| #31774031 | 2 |
| D8×Dic271 | 2 |
| #31773977 | 2 |
| #31773947 | 2 |
| #447×C271 | 2 |
| #3100 | 271 |