Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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. #31774525 | C2 | semidirect |
| 2. #31774197 | C2 | semidirect |
| 3. #31774197 | C2 | semidirect |
| 4. #31774187 | C2 | semidirect |
| 5. #31774177 | C2 | semidirect |
| 6. #31773940 | C2 | semidirect |
| 7. #31773933 | C2 | semidirect |
| 8. #31773924 | C2 | semidirect |
| 14. #22576160 | C22 | semidirect |
| 16. #22576152 | 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 |
| 27. C4⋊(C271⋊C8) | C22 | semidirect |
| 28. C4⋊(C271⋊C8) | C22 | semidirect |
| 60. C2×D4×C271 | Q8 | semidirect |
| 124. C271 | #3081 | semidirect |
| 170. C2×D4 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774525 | 2 |
| #31774197 | 2 |
| #31774187 | 2 |
| #31774177 | 2 |
| #31773940 | 2 |
| #31773933 | 2 |
| #31773924 | 2 |
| #31773902 | 2 |
| C2×#22576081 | 2 |
| #518×C271 | 2 |
| #3081 | 271 |