Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 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. C2×#22576182 | C2 | semidirect |
| 2. C2×#22576179 | C2 | semidirect |
| 3. #31774565 | C2 | semidirect |
| 4. #31774272 | C2 | semidirect |
| 5. #31774134 | C2 | semidirect |
| 6. #31774096 | C2 | semidirect |
| 7. #31774043 | C2 | semidirect |
| 8. #31774040 | C2 | semidirect |
| 9. #31773991 | C2 | semidirect |
| 10. C8×C22⋊D271 | C2 | semidirect |
| 11. #466×C271 | C2 | semidirect |
| 56. Dic1084 | D4 | semidirect |
| 134. Dic271 | #135 | semidirect |
| 142. C271 | #3287 | semidirect |
| 149. #466 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576182 | 2 |
| C2×#22576179 | 2 |
| #31774565 | 2 |
| #31774272 | 2 |
| #31774134 | 2 |
| #31774096 | 2 |
| #31774043 | 2 |
| #31774040 | 2 |
| #31773991 | 2 |
| C8×C22⋊D271 | 2 |
| #466×C271 | 2 |
| #3287 | 271 |