Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#22576189 | C2 | semidirect |
| 2. C2×#22576184 | C2 | semidirect |
| 3. #31774445 | C2 | semidirect |
| 4. #124×D271 | C2 | semidirect |
| 5. #31774292 | C2 | semidirect |
| 6. #31774291 | C2 | semidirect |
| 7. #31774284 | C2 | semidirect |
| 8. #31774280 | C2 | semidirect |
| 9. #31774278 | C2 | semidirect |
| 10. #31773849 | C2 | semidirect |
| 11. #496×C271 | C2 | semidirect |
| 17. C2×Dic1084 | C22 | semidirect |
| 18. C2×#16864644 | C22 | semidirect |
| 21. C2×#16864642 | C22 | semidirect |
| 24. #22576160 | C22 | semidirect |
| 28. #22576147 | C22 | semidirect |
| 34. #22576071 | C22 | semidirect |
| 35. C8×Dic271 | C22 | semidirect |
| 36. C2×SD16×C271 | C22 | semidirect |
| 38. #127×C271 | C22 | semidirect |
| 40. #97×C271 | C22 | semidirect |
| 62. #16864637 | D4 | semidirect |
| 134. C271 | #3153 | semidirect |
| 143. #496 | D271 | semidirect |
| 157. C2×SD16 | C2×D271 | semidirect |
| 162. #127 | C2×D271 | semidirect |
| 174. #97 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576189 | 2 |
| C2×#22576184 | 2 |
| #31774445 | 2 |
| #124×D271 | 2 |
| #31774292 | 2 |
| #31774291 | 2 |
| #31774284 | 2 |
| #31774280 | 2 |
| #31774278 | 2 |
| #31773849 | 2 |
| #496×C271 | 2 |
| #3153 | 271 |