Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #31774705 | C2 | semidirect |
| 2. #31774699 | C2 | semidirect |
| 3. #31774282 | C2 | semidirect |
| 4. #31774169 | C2 | semidirect |
| 5. #31774167 | C2 | semidirect |
| 6. #31774162 | C2 | semidirect |
| 7. #31774073 | C2 | semidirect |
| 8. #31774070 | C2 | semidirect |
| 9. #31774014 | C2 | semidirect |
| 10. #31774012 | C2 | semidirect |
| 11. #578×C271 | C2 | semidirect |
| 18. #22576185 | C22 | semidirect |
| 23. C2×#16864641 | C22 | semidirect |
| 26. #22576167 | C22 | semidirect |
| 28. #22576149 | C22 | semidirect |
| 29. #22576096 | C22 | semidirect |
| 30. #22576095 | C22 | semidirect |
| 31. #22576087 | C22 | semidirect |
| 32. #22576087 | C22 | semidirect |
| 34. #22576079 | C22 | semidirect |
| 35. #22576076 | C22 | semidirect |
| 36. C8×Dic271 | C22 | semidirect |
| 37. 2−1+4×C271 | C22 | semidirect |
| 39. #137×C271 | C22 | semidirect |
| 43. C2×Q16×C271 | C22 | semidirect |
| 44. #131×C271 | C22 | semidirect |
| 149. C271 | #3290 | semidirect |
| 151. #578 | D271 | semidirect |
| 162. 2−1+4 | C2×D271 | semidirect |
| 167. #137 | C2×D271 | semidirect |
| 178. C2×Q16 | C2×D271 | semidirect |
| 185. #131 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774705 | 2 |
| #31774699 | 2 |
| #31774282 | 2 |
| #31774169 | 2 |
| #31774167 | 2 |
| #31774162 | 2 |
| #31774073 | 2 |
| #31774070 | 2 |
| #31774014 | 2 |
| #31774012 | 2 |
| #578×C271 | 2 |
| #3290 | 271 |