Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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. #31773920 | C2 | semidirect |
| 5. C4×Dic271⋊C4 | C2 | semidirect |
| 6. #31773656 | C2 | semidirect |
| 7. #339×C271 | C2 | semidirect |
| 10. #22576125 | C4 | semidirect |
| 11. #22576125 | C4 | semidirect |
| 12. #22576122 | C4 | semidirect |
| 13. #22576122 | C4 | semidirect |
| 71. Dic542 | C4⋊C4 | semidirect |
| 73. D1084 | C4⋊C4 | semidirect |
| 124. Dic271 | #104 | semidirect |
| 131. C271 | #1806 | semidirect |
| 139. #339 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774365 | 2 |
| #31773920 | 2 |
| C2×#22576088 | 2 |
| C2×#22576086 | 2 |
| C4×Dic271⋊C4 | 2 |
| #31773656 | 2 |
| #339×C271 | 2 |
| #1806 | 271 |