Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31774525 | C2 | semidirect |
| 3. #31774262 | C2 | semidirect |
| 4. #31774257 | C2 | semidirect |
| 5. #31774252 | C2 | semidirect |
| 6. #31774244 | C2 | semidirect |
| 7. #31773903 | C2 | semidirect |
| 8. #31773899 | C2 | semidirect |
| 9. #31773894 | C2 | semidirect |
| 10. C2×#22576082 | C2 | semidirect |
| 11. #405×C271 | C2 | semidirect |
| 14. #22576160 | C22 | semidirect |
| 17. #22576152 | C22 | semidirect |
| 26. #22576085 | C22 | semidirect |
| 27. #22576085 | C22 | semidirect |
| 28. #22576085 | C22 | semidirect |
| 33. #22576082 | C22 | semidirect |
| 34. #22576082 | C22 | semidirect |
| 35. #22576082 | C22 | semidirect |
| 39. #97×C271 | C22 | semidirect |
| 40. C4×C8×C271 | C22 | semidirect |
| 135. C271 | #3136 | semidirect |
| 147. #405 | D271 | semidirect |
| 175. #97 | C2×D271 | semidirect |
| 176. C4×C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774525 | 2 |
| #31774466 | 2 |
| #31774262 | 2 |
| #31774257 | 2 |
| #31774252 | 2 |
| #31774244 | 2 |
| #31773903 | 2 |
| #31773899 | 2 |
| #31773894 | 2 |
| C2×#22576082 | 2 |
| #405×C271 | 2 |
| #3136 | 271 |