Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. #22553643 | C2 | direct (N × H) |
| 4. C2×#16862178 | C2 | semidirect |
| 5. C2×#16862171 | C2 | semidirect |
| 18. #16862178 | C22 | semidirect |
| 19. #16862171 | C22 | semidirect |
| 83. C2×C131 | #483 | semidirect |
| 87. C131 | C2×#483 | semidirect |
| 171. C2 | #22553643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862225 | 2 |
| C22×C4⋊Dic131 | 2 |
| #22553643 | 2 |
| C2×#16862178 | 2 |
| C2×#16862171 | 2 |
| C2×C22⋊C8×C131 | 2 |
| C2×#483 | 131 |