Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
274 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22553050 | C2 | semidirect |
| 5. C22×Dic262 | C4 | semidirect |
| 8. #16862225 | C4 | semidirect |
| 10. C2×C4⋊Dic131 | C4 | semidirect |
| 93. C131 | #1511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862225 | 2 |
| #22553175 | 2 |
| #22553050 | 2 |
| #407×C131 | 2 |
| #1511 | 131 |