Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #31773920 | C2 | semidirect |
| 3. C2×#22576088 | C2 | semidirect |
| 4. C2×#22576087 | C2 | semidirect |
| 5. C2×#22576086 | C2 | semidirect |
| 6. C42×Dic271 | C2 | semidirect |
| 7. C2×#104×C271 | C2 | semidirect |
| 10. #22576158 | C4 | semidirect |
| 11. #22576156 | C4 | semidirect |
| 12. #22576149 | C4 | semidirect |
| 13. #22576147 | C4 | semidirect |
| 49. C4×Dic271 | D4 | semidirect |
| 64. C42×C271 | D4 | semidirect |
| 119. Dic271 | #104 | semidirect |
| 126. C271 | #1962 | semidirect |
| 133. C2×#104 | D271 | semidirect |
| 191. C42 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774443 | 2 |
| #31773920 | 2 |
| C2×#22576088 | 2 |
| C2×#22576087 | 2 |
| C2×#22576086 | 2 |
| C42×Dic271 | 2 |
| C2×#104×C271 | 2 |
| #1962 | 271 |