Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #31774663 | C2 | semidirect |
| 3. #31774018 | C2 | semidirect |
| 4. #31774013 | C2 | semidirect |
| 5. C2×#22576086 | C2 | semidirect |
| 6. M16×Dic271 | C2 | semidirect |
| 7. #430×C271 | C2 | semidirect |
| 9. #22576193 | C4 | semidirect |
| 10. #22576188 | C4 | semidirect |
| 12. #22576168 | C22 | semidirect |
| 17. #22576086 | C22 | semidirect |
| 18. #22576086 | C22 | semidirect |
| 19. #22576070 | C22 | semidirect |
| 20. C8×Dic271 | C22 | semidirect |
| 23. #108×C271 | C22 | semidirect |
| 33. Dic1084 | C2×C4 | semidirect |
| 34. #16864643 | C2×C4 | semidirect |
| 35. D2168 | C2×C4 | semidirect |
| 85. C271 | #2956 | semidirect |
| 91. #430 | D271 | semidirect |
| 105. #108 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774697 | 2 |
| #31774663 | 2 |
| #31774018 | 2 |
| #31774013 | 2 |
| C2×#22576086 | 2 |
| M16×Dic271 | 2 |
| #430×C271 | 2 |
| #2956 | 271 |