Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #31774235 | C2 | semidirect |
| 3. #31774194 | C2 | semidirect |
| 4. #31774099 | C2 | semidirect |
| 6. #31773995 | C2 | semidirect |
| 7. C4×#16864641 | C2 | semidirect |
| 8. #31773958 | C2 | semidirect |
| 9. #541×C271 | C2 | semidirect |
| 18. #22576093 | C22 | semidirect |
| 19. #22576091 | C22 | semidirect |
| 20. C4⋊(C271⋊C8) | C22 | semidirect |
| 21. #22576084 | C22 | semidirect |
| 22. #22576084 | C22 | semidirect |
| 26. #22576071 | C22 | semidirect |
| 27. C4×C271⋊C8 | C22 | semidirect |
| 28. C4⋊Q8×C271 | C22 | semidirect |
| 31. #125×C271 | C22 | semidirect |
| 33. C4×Q8×C271 | C22 | semidirect |
| 102. C271 | #3123 | semidirect |
| 104. #541 | D271 | semidirect |
| 116. C4⋊Q8 | C2×D271 | semidirect |
| 119. #125 | C2×D271 | semidirect |
| 121. C4×Q8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774371 | 2 |
| #31774235 | 2 |
| #31774194 | 2 |
| #31774099 | 2 |
| #31774047 | 2 |
| #31773995 | 2 |
| C4×#16864641 | 2 |
| #31773958 | 2 |
| #541×C271 | 2 |
| #3123 | 271 |