Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774617 | C2 | semidirect |
| 2. #31774300 | C2 | semidirect |
| 3. #31774232 | C2 | semidirect |
| 4. #31774218 | C2 | semidirect |
| 5. #31774179 | C2 | semidirect |
| 6. #31774177 | C2 | semidirect |
| 7. #31774141 | C2 | semidirect |
| 8. C4×#16864642 | C2 | semidirect |
| 9. #31773975 | C2 | semidirect |
| 10. #31773937 | C2 | semidirect |
| 82. C271⋊C8 | #41 | semidirect |
| 122. C271 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774617 | 2 |
| #31774300 | 2 |
| #31774232 | 2 |
| #31774218 | 2 |
| #31774179 | 2 |
| #31774177 | 2 |
| #31774141 | 2 |
| C4×#16864642 | 2 |
| #31773975 | 2 |
| #31773937 | 2 |
| #547×C271 | 2 |
| #3353 | 271 |