Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22576181 | C2 | semidirect |
| 2. #31774448 | C2 | semidirect |
| 3. C4×#16864653 | C2 | semidirect |
| 4. #31774122 | C2 | semidirect |
| 5. #31774114 | C2 | semidirect |
| 6. #31774104 | C2 | semidirect |
| 7. #31774098 | C2 | semidirect |
| 8. #31774092 | C2 | semidirect |
| 9. C4⋊C8×D271 | C2 | semidirect |
| 10. #31773892 | C2 | semidirect |
| 11. #461×C271 | C2 | semidirect |
| 47. #16864653 | D4 | semidirect |
| 136. C4×C271 | #135 | semidirect |
| 150. C271 | #3035 | semidirect |
| 158. #461 | D271 | semidirect |
| 292. C4 | #22576181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576181 | 2 |
| #31774448 | 2 |
| C4×#16864653 | 2 |
| #31774122 | 2 |
| #31774114 | 2 |
| #31774104 | 2 |
| #31774098 | 2 |
| #31774092 | 2 |
| C4⋊C8×D271 | 2 |
| #31773892 | 2 |
| #461×C271 | 2 |
| #3035 | 271 |