Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
504 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 197 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. #22553210 | C2 | semidirect |
| 4. #22553179 | C2 | semidirect |
| 6. C4×C4⋊Dic131 | C2 | semidirect |
| 7. #22553163 | C2 | semidirect |
| 9. #16862205 | C4 | semidirect |
| 94. C131 | #2347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862205 | 2 |
| #22553210 | 2 |
| #22553206 | 2 |
| #22553179 | 2 |
| #22553172 | 2 |
| C4×C4⋊Dic131 | 2 |
| #22553163 | 2 |
| C4×C22⋊C4×C131 | 2 |
| #2347 | 131 |