Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. #22553238 | C2 | semidirect |
| 3. #22553213 | C2 | semidirect |
| 4. #22553191 | C2 | semidirect |
| 5. #22553177 | C2 | semidirect |
| 6. C4×C22⋊Dic131 | C2 | semidirect |
| 7. C22×C4⋊C4×C131 | C2 | semidirect |
| 92. C131 | #2504 | semidirect |
| 95. C22×C4⋊C4 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862220 | 2 |
| #22553238 | 2 |
| #22553213 | 2 |
| #22553191 | 2 |
| #22553177 | 2 |
| C4×C22⋊Dic131 | 2 |
| C22×C4⋊C4×C131 | 2 |
| #2504 | 131 |