Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16862171 | C2 | semidirect |
| 4. #22553075 | C2 | semidirect |
| 8. #16862225 | C4 | semidirect |
| 93. C131 | #1873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862225 | 2 |
| C2×#16862205 | 2 |
| C2×#16862171 | 2 |
| #22553075 | 2 |
| C2×C22⋊C8×C131 | 2 |
| #1873 | 131 |