Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 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×#22576192 | C2 | semidirect |
| 3. C2×Q16×D271 | C2 | semidirect |
| 4. #31774472 | C2 | semidirect |
| 5. #31774290 | C2 | semidirect |
| 6. #31774289 | C2 | semidirect |
| 7. #31774282 | C2 | semidirect |
| 8. #31774281 | C2 | semidirect |
| 9. #31774275 | C2 | semidirect |
| 10. #31773851 | C2 | semidirect |
| 11. #494×C271 | C2 | semidirect |
| 121. C271 | #3156 | semidirect |
| 132. #494 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576192 | 2 |
| C2×#22576183 | 2 |
| C2×Q16×D271 | 2 |
| #31774472 | 2 |
| #31774290 | 2 |
| #31774289 | 2 |
| #31774282 | 2 |
| #31774281 | 2 |
| #31774275 | 2 |
| #31773851 | 2 |
| #494×C271 | 2 |
| #3156 | 271 |