Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22553089 | C2 | direct (N × H) |
| 7. #16862186 | C4 | semidirect |
| 9. C2×C131⋊C16 | C4 | semidirect |
| 13. M32×C131 | C4 | semidirect |
| 15. C2×C16×C131 | C4 | semidirect |
| 22. C131⋊C16 | C2×C4 | semidirect |
| 30. C16×C131 | C2×C4 | semidirect |
| 56. C2×C131 | #347 | semidirect |
| 58. C131 | C2×#347 | semidirect |
| 69. M32 | Dic131 | semidirect |
| 72. C2×C16 | Dic131 | semidirect |
| 89. C16 | C2×Dic131 | semidirect |
| 115. C2 | #22553089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862186 | 2 |
| C2×#16862156 | 2 |
| #22553089 | 2 |
| C2×M32×C131 | 2 |
| C2×#347 | 131 |