Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #22553101 | C2 | direct (N × H) |
| 5. C23×Dic131 | C4 | semidirect |
| 9. #16862227 | C4 | semidirect |
| 13. C2×C22⋊Dic131 | C4 | semidirect |
| 25. C22×Dic131 | C2×C4 | semidirect |
| 34. C22⋊Dic131 | C2×C4 | semidirect |
| 103. C2×C131 | #352 | semidirect |
| 105. C131 | C2×#352 | semidirect |
| 209. C2 | #22553101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862227 | 2 |
| C2×#16862163 | 2 |
| #22553101 | 2 |
| C2×#99×C131 | 2 |
| C2×#352 | 131 |