Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22576180 | C2 | semidirect |
| 2. C2×#22576168 | C2 | semidirect |
| 3. #31774478 | C2 | semidirect |
| 4. #31774475 | C2 | semidirect |
| 5. #31774154 | C2 | semidirect |
| 6. #31774149 | C2 | semidirect |
| 7. #31774129 | C2 | semidirect |
| 8. #31774125 | C2 | semidirect |
| 9. C2×#22576091 | C2 | semidirect |
| 10. #31773899 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 63. C2×C271⋊C8 | D4 | semidirect |
| 152. C271 | #3060 | semidirect |
| 164. #417 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576180 | 2 |
| C2×#22576168 | 2 |
| #31774478 | 2 |
| #31774475 | 2 |
| #31774154 | 2 |
| #31774149 | 2 |
| #31774129 | 2 |
| #31774125 | 2 |
| C2×#22576091 | 2 |
| #31773899 | 2 |
| #417×C271 | 2 |
| #3060 | 271 |