Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #31774374 | C2 | semidirect |
| 3. #31773997 | C2 | semidirect |
| 4. C4×#16864642 | C2 | semidirect |
| 5. #31773933 | C2 | semidirect |
| 6. #31773905 | C2 | semidirect |
| 8. #31773853 | C2 | semidirect |
| 11. C2×#16864642 | C4 | semidirect |
| 16. C4×Dic542 | C22 | semidirect |
| 20. #22576093 | C22 | semidirect |
| 21. #22576091 | C22 | semidirect |
| 22. #22576083 | C22 | semidirect |
| 24. #22576071 | C22 | semidirect |
| 25. C4×C271⋊C8 | C22 | semidirect |
| 34. C2×Dic542 | C2×C4 | semidirect |
| 37. #16864642 | C2×C4 | semidirect |
| 38. #16864642 | C2×C4 | semidirect |
| 40. C2×C271⋊C8 | C2×C4 | semidirect |
| 103. C271 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864642 | 2 |
| #31774374 | 2 |
| #31773997 | 2 |
| C4×#16864642 | 2 |
| #31773933 | 2 |
| #31773905 | 2 |
| #31773902 | 2 |
| #31773853 | 2 |
| #518×C271 | 2 |
| #2949 | 271 |