Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 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×#22576208 | C2 | semidirect |
| 2. C2×#22576180 | C2 | semidirect |
| 3. #31774475 | C2 | semidirect |
| 4. #31774058 | C2 | semidirect |
| 5. #31774051 | C2 | semidirect |
| 6. #31774041 | C2 | semidirect |
| 7. #31774034 | C2 | semidirect |
| 8. #31773899 | C2 | semidirect |
| 9. C2×#22576084 | C2 | semidirect |
| 10. #31773865 | C2 | semidirect |
| 11. C2×#137×C271 | C2 | semidirect |
| 52. #16864654 | D4 | semidirect |
| 86. C2×Q8×C271 | D4 | semidirect |
| 169. C271 | #3013 | semidirect |
| 172. C2×#137 | D271 | semidirect |
| 233. C2×Q8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576208 | 2 |
| C2×#22576180 | 2 |
| #31774475 | 2 |
| #31774058 | 2 |
| #31774051 | 2 |
| #31774041 | 2 |
| #31774034 | 2 |
| #31773899 | 2 |
| C2×#22576084 | 2 |
| #31773865 | 2 |
| C2×#137×C271 | 2 |
| #3013 | 271 |