Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 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. #31774697 | C2 | semidirect |
| 2. C2×#22576182 | C2 | semidirect |
| 3. C2×#22576166 | C2 | semidirect |
| 4. #31774173 | C2 | semidirect |
| 5. #31774168 | C2 | semidirect |
| 6. #31774161 | C2 | semidirect |
| 7. #31773879 | C2 | semidirect |
| 8. C2×#108×C271 | C2 | semidirect |
| 20. C2×Dic1084 | C22 | semidirect |
| 21. C2×#16864643 | C22 | semidirect |
| 22. C2×D2168 | C22 | semidirect |
| 30. #22576078 | C22 | semidirect |
| 31. #22576076 | C22 | semidirect |
| 34. #108×C271 | C22 | semidirect |
| 35. #108×C271 | C22 | semidirect |
| 132. C271 | #3067 | semidirect |
| 140. C2×#108 | D271 | semidirect |
| 165. #108 | C2×D271 | semidirect |
| 166. #108 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774697 | 2 |
| C2×#22576182 | 2 |
| C2×#22576166 | 2 |
| #31774173 | 2 |
| #31774168 | 2 |
| #31774161 | 2 |
| #31773879 | 2 |
| C2×#108×C271 | 2 |
| #3067 | 271 |