Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
548 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 213 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. #22553208 | C2 | semidirect |
| 3. #22553197 | C2 | semidirect |
| 5. C4⋊C4×Dic131 | C2 | semidirect |
| 10. C2×C4⋊Dic131 | C4 | semidirect |
| 96. C131 | #2345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic131 | 2 |
| #22553208 | 2 |
| #22553197 | 2 |
| #22553170 | 2 |
| C4⋊C4×Dic131 | 2 |
| C22⋊C4×Dic131 | 2 |
| C4×C22⋊Dic131 | 2 |
| #380×C131 | 2 |
| #2345 | 131 |