Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22576191 | C2 | semidirect |
| 2. C2×#22576190 | C2 | semidirect |
| 4. C22×#16864644 | C2 | semidirect |
| 5. #31774473 | C2 | semidirect |
| 6. #31774292 | C2 | semidirect |
| 7. #31774289 | C2 | semidirect |
| 8. #31774279 | C2 | semidirect |
| 9. #31774276 | C2 | semidirect |
| 10. #31773853 | C2 | semidirect |
| 11. #536×C271 | C2 | semidirect |
| 143. C271 | #3156 | semidirect |
| 150. #536 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576191 | 2 |
| C2×#22576190 | 2 |
| C2×#22576180 | 2 |
| C22×#16864644 | 2 |
| #31774473 | 2 |
| #31774292 | 2 |
| #31774289 | 2 |
| #31774279 | 2 |
| #31774276 | 2 |
| #31773853 | 2 |
| #536×C271 | 2 |
| #3156 | 271 |