Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22553048 | C2 | direct (N × H) |
| 5. C22×Dic262 | C4 | semidirect |
| 9. #16862225 | C4 | semidirect |
| 11. C2×C4⋊Dic131 | C4 | semidirect |
| 22. C2×Dic262 | C2×C4 | semidirect |
| 28. C4⋊Dic131 | C2×C4 | semidirect |
| 96. C2×C131 | #328 | semidirect |
| 100. C131 | C2×#328 | semidirect |
| 197. C2 | #22553048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862225 | 2 |
| C2×C22⋊(C131⋊C8) | 2 |
| #22553048 | 2 |
| C2×#95×C131 | 2 |
| C2×#328 | 131 |