Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #31774194 | C2 | semidirect |
| 3. #31774194 | C2 | semidirect |
| 4. #31774184 | C2 | semidirect |
| 5. #31774174 | C2 | semidirect |
| 6. #31773937 | C2 | semidirect |
| 7. #31773933 | C2 | semidirect |
| 8. #31773924 | C2 | semidirect |
| 11. #544×C271 | C2 | 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 |
| 34. C4⋊Q8×C271 | C22 | semidirect |
| 36. #125×C271 | C22 | semidirect |
| 44. C2×D1084 | Q8 | semidirect |
| 124. C271 | #3081 | semidirect |
| 126. #544 | D271 | semidirect |
| 141. C4⋊Q8 | C2×D271 | semidirect |
| 143. #125 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774371 | 2 |
| #31774194 | 2 |
| #31774184 | 2 |
| #31774174 | 2 |
| #31773937 | 2 |
| #31773933 | 2 |
| #31773924 | 2 |
| #31773901 | 2 |
| C2×#22576080 | 2 |
| #544×C271 | 2 |
| #3081 | 271 |