Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 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. C22×C4⋊Dic131 | C2 | semidirect |
| 3. #22553626 | C2 | direct (N × H) |
| 4. C2×#16862180 | C2 | semidirect |
| 5. C2×#16862168 | C2 | semidirect |
| 6. C2×C22⋊C8×C131 | C2 | semidirect |
| 16. C2×C4⋊Dic131 | C22 | semidirect |
| 18. #16862180 | C22 | semidirect |
| 19. #16862168 | C22 | semidirect |
| 22. C22⋊C8×C131 | C22 | semidirect |
| 90. C2×C131 | #480 | semidirect |
| 95. C131 | C2×#480 | semidirect |
| 102. C2×C22⋊C8 | D131 | semidirect |
| 118. C22⋊C8 | C2×D131 | semidirect |
| 187. C2 | #22553626 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862220 | 2 |
| C22×C4⋊Dic131 | 2 |
| #22553626 | 2 |
| C2×#16862180 | 2 |
| C2×#16862168 | 2 |
| C2×C22⋊C8×C131 | 2 |
| C2×#480 | 131 |