Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774447 | C2 | semidirect |
| 2. C4×#16864654 | C2 | semidirect |
| 3. #31774222 | C2 | semidirect |
| 4. #31774183 | C2 | semidirect |
| 5. #31774178 | C2 | semidirect |
| 6. #31774098 | C2 | semidirect |
| 7. #31774093 | C2 | semidirect |
| 8. #31774044 | C2 | semidirect |
| 9. #31774010 | C2 | semidirect |
| 10. #31773999 | C2 | semidirect |
| 11. #432×C271 | C2 | semidirect |
| 87. Dic542 | #41 | semidirect |
| 93. D1084 | #41 | semidirect |
| 144. C271 | #3115 | semidirect |
| 156. #432 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774447 | 2 |
| C4×#16864654 | 2 |
| #31774222 | 2 |
| #31774183 | 2 |
| #31774178 | 2 |
| #31774098 | 2 |
| #31774093 | 2 |
| #31774044 | 2 |
| #31774010 | 2 |
| #31773999 | 2 |
| #432×C271 | 2 |
| #3115 | 271 |