Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22576186 | C2 | semidirect |
| 2. #31774464 | C2 | semidirect |
| 3. #31774372 | C2 | semidirect |
| 4. #31774110 | C2 | semidirect |
| 5. #31774090 | C2 | semidirect |
| 6. #31773923 | C2 | semidirect |
| 7. #31773902 | C2 | semidirect |
| 8. #31773894 | C2 | semidirect |
| 9. C22×D8×C271 | C2 | semidirect |
| 12. C2×#16864642 | C22 | semidirect |
| 13. C2×#16864639 | C22 | semidirect |
| 15. #22576156 | C22 | semidirect |
| 16. #22576147 | C22 | semidirect |
| 20. D4×Dic271 | C22 | semidirect |
| 24. Dic271⋊C8 | C22 | semidirect |
| 25. #22576085 | C22 | semidirect |
| 26. #22576082 | C22 | semidirect |
| 27. #22576081 | C22 | semidirect |
| 60. C2×D4×C271 | D4 | semidirect |
| 121. C271 | #3041 | semidirect |
| 124. C22×D8 | D271 | semidirect |
| 168. C2×D4 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| #31774464 | 2 |
| #31774372 | 2 |
| #31774110 | 2 |
| #31774090 | 2 |
| #31773923 | 2 |
| #31773902 | 2 |
| #31773894 | 2 |
| C22×D8×C271 | 2 |
| #3041 | 271 |