Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #31774372 | C2 | semidirect |
| 3. #31773913 | C2 | semidirect |
| 4. #31773870 | C2 | semidirect |
| 5. #31773669 | C2 | semidirect |
| 6. #31773653 | C2 | semidirect |
| 7. #418×C271 | C2 | semidirect |
| 11. C2×#16864642 | C4 | semidirect |
| 12. C2×#16864639 | C4 | semidirect |
| 29. C2×Dic542 | C2×C4 | semidirect |
| 30. C2×D1084 | C2×C4 | semidirect |
| 38. C2×C271⋊C8 | C2×C4 | semidirect |
| 115. C271 | #1904 | semidirect |
| 120. #418 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| #31774372 | 2 |
| #31773913 | 2 |
| #31773870 | 2 |
| #31773669 | 2 |
| #31773653 | 2 |
| #418×C271 | 2 |
| #1904 | 271 |