Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22576180 | C2 | semidirect |
| 2. #31774447 | C2 | semidirect |
| 3. #31774279 | C2 | semidirect |
| 4. #31774276 | C2 | semidirect |
| 5. #31774273 | C2 | semidirect |
| 6. #31774271 | C2 | semidirect |
| 7. #31774269 | C2 | semidirect |
| 8. C2×C4×C271⋊C8 | C2 | semidirect |
| 9. #532×C271 | C2 | semidirect |
| 42. C2×C271⋊C8 | D4 | semidirect |
| 93. C4×C271 | #135 | semidirect |
| 101. C271 | #3147 | semidirect |
| 105. #532 | D271 | semidirect |
| 196. C4 | #22576180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576180 | 2 |
| #31774447 | 2 |
| #31774279 | 2 |
| #31774276 | 2 |
| #31774273 | 2 |
| #31774271 | 2 |
| #31774269 | 2 |
| C2×C4×C271⋊C8 | 2 |
| #532×C271 | 2 |
| #3147 | 271 |