Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22576207 | C2 | semidirect |
| 2. #31774697 | C2 | semidirect |
| 3. #31774695 | C2 | semidirect |
| 4. #31774473 | C2 | semidirect |
| 5. #31774081 | C2 | semidirect |
| 6. #31774071 | C2 | semidirect |
| 7. #31773915 | C2 | semidirect |
| 8. C2×#22576078 | C2 | semidirect |
| 9. #421×C271 | C2 | semidirect |
| 23. #22576193 | C22 | semidirect |
| 25. #22576190 | C22 | semidirect |
| 27. #22576188 | C22 | semidirect |
| 29. #22576185 | C22 | semidirect |
| 33. #22576160 | C22 | semidirect |
| 34. #22576148 | C22 | semidirect |
| 37. #22576088 | C22 | semidirect |
| 38. #22576078 | C22 | semidirect |
| 42. #104×C271 | C22 | semidirect |
| 185. C271 | #3020 | semidirect |
| 194. #421 | D271 | semidirect |
| 227. #104 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576207 | 2 |
| #31774697 | 2 |
| #31774695 | 2 |
| #31774473 | 2 |
| #31774081 | 2 |
| #31774071 | 2 |
| #31773915 | 2 |
| C2×#22576078 | 2 |
| #421×C271 | 2 |
| #3020 | 271 |