Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22576179 | C2 | semidirect |
| 2. #31774541 | C2 | semidirect |
| 3. #31774280 | C2 | semidirect |
| 4. #31774138 | C2 | semidirect |
| 5. #31774130 | C2 | semidirect |
| 6. #31774110 | C2 | semidirect |
| 7. #31774048 | C2 | semidirect |
| 8. #31774039 | C2 | semidirect |
| 9. D8×Dic271 | C2 | semidirect |
| 10. C8×C22⋊D271 | C2 | semidirect |
| 11. C22×D8×C271 | C2 | semidirect |
| 12. C2×#16864653 | C22 | semidirect |
| 14. C2×Dic1084 | C22 | semidirect |
| 15. C2×#16864642 | C22 | semidirect |
| 16. C2×#16864642 | C22 | semidirect |
| 17. C2×C8×D271 | C22 | semidirect |
| 18. #22576147 | C22 | semidirect |
| 22. #22576131 | C22 | semidirect |
| 24. D4×Dic271 | C22 | semidirect |
| 27. #22576094 | C22 | semidirect |
| 28. Dic271⋊C8 | C22 | semidirect |
| 29. #22576085 | C22 | semidirect |
| 30. #22576081 | C22 | semidirect |
| 31. #22576081 | C22 | semidirect |
| 33. (C2×D271)⋊C8 | C22 | semidirect |
| 34. C8×Dic271 | C22 | semidirect |
| 76. D8×C271 | D4 | semidirect |
| 123. C22×C271 | #135 | semidirect |
| 143. C271 | #3280 | semidirect |
| 146. C22×D8 | D271 | semidirect |
| 206. D8 | C22⋊D271 | semidirect |
| 270. C22 | #22576179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576179 | 2 |
| #31774541 | 2 |
| #31774280 | 2 |
| #31774138 | 2 |
| #31774130 | 2 |
| #31774110 | 2 |
| #31774048 | 2 |
| #31774039 | 2 |
| D8×Dic271 | 2 |
| C8×C22⋊D271 | 2 |
| C22×D8×C271 | 2 |
| #3280 | 271 |