Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 9. #22576159 | C4 | semidirect |
| 10. #22576159 | C4 | semidirect |
| 11. #22576151 | C4 | semidirect |
| 12. #22576151 | C4 | semidirect |
| 33. #16864638 | Q8 | semidirect |
| 55. M16×C271 | Q8 | semidirect |
| 114. C271 | #1986 | semidirect |
| 152. M16 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| M16×Dic271 | 2 |
| C4×Dic271⋊C4 | 2 |
| #31773658 | 2 |
| #31773657 | 2 |
| #31773656 | 2 |
| #339×C271 | 2 |
| #1986 | 271 |