Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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. #31774380 | C2 | semidirect |
| 2. #31774218 | C2 | semidirect |
| 3. #31774218 | C2 | semidirect |
| 4. #31774213 | C2 | semidirect |
| 5. #31774208 | C2 | semidirect |
| 6. #31773940 | C2 | semidirect |
| 7. #31773933 | C2 | semidirect |
| 8. #31773902 | C2 | semidirect |
| 9. C2×#22576081 | C2 | semidirect |
| 10. #31773864 | C2 | semidirect |
| 18. #22576119 | C22 | semidirect |
| 20. C2×C4⋊Dic271 | C22 | semidirect |
| 21. #22576093 | C22 | semidirect |
| 22. #22576093 | C22 | semidirect |
| 23. #22576093 | C22 | semidirect |
| 24. #22576091 | C22 | semidirect |
| 25. #22576091 | C22 | semidirect |
| 26. #22576091 | C22 | semidirect |
| 31. C22⋊(C271⋊C8) | C22 | semidirect |
| 32. C22⋊(C271⋊C8) | C22 | semidirect |
| 134. C271 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774380 | 2 |
| #31774218 | 2 |
| #31774213 | 2 |
| #31774208 | 2 |
| #31773940 | 2 |
| #31773933 | 2 |
| #31773902 | 2 |
| C2×#22576081 | 2 |
| #31773864 | 2 |
| #535×C271 | 2 |
| #3096 | 271 |