Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22576180 | C2 | semidirect |
| 3. #31774443 | C2 | semidirect |
| 4. #31774282 | C2 | semidirect |
| 5. #31774280 | C2 | semidirect |
| 6. #31774278 | C2 | semidirect |
| 7. #31774275 | C2 | semidirect |
| 8. #31774272 | C2 | semidirect |
| 9. #31774268 | C2 | semidirect |
| 10. C2×C8×Dic271 | C2 | semidirect |
| 11. C2×#135×C271 | C2 | semidirect |
| 55. C2×C271⋊C8 | D4 | semidirect |
| 74. C2×C8×C271 | D4 | semidirect |
| 119. Dic271 | #135 | semidirect |
| 125. C271 | #3147 | semidirect |
| 129. C2×#135 | D271 | semidirect |
| 194. C2×C8 | C22⋊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×#22576180 | 2 |
| #31774443 | 2 |
| #31774282 | 2 |
| #31774280 | 2 |
| #31774278 | 2 |
| #31774275 | 2 |
| #31774272 | 2 |
| #31774268 | 2 |
| C2×C8×Dic271 | 2 |
| C2×#135×C271 | 2 |
| #3147 | 271 |