Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
600 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 349 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. C2×#16862177 | C2 | direct (N × H) |
| 6. C22×C131⋊C8 | C4 | semidirect |
| 10. #16862177 | C22 | direct (N × H) |
| 17. C2×C131⋊C8 | C2×C4 | semidirect |
| 32. C131⋊C8 | C22×C4 | semidirect |
| 44. C22×C131 | #106 | semidirect |
| 54. C2×C131 | C2×#106 | semidirect |
| 58. C131 | C22×#106 | semidirect |
| 103. C22 | #16862177 | direct (N × H) |
| 113. C2 | C2×#16862177 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C131⋊C8 | 2 |
| C22×C4⋊Dic131 | 2 |
| C2×#16862177 | 2 |
| C22×C4⋊C4×C131 | 2 |
| C22×#106 | 131 |