Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×C131⋊#95 | C2 | semidirect |
| 3. #22553047 | C2 | direct (N × H) |
| 4. C2×C22⋊C8×C131 | C2 | semidirect |
| 5. C22×D524 | C4 | semidirect |
| 10. #16862220 | C4 | semidirect |
| 12. C2×C4⋊Dic131 | C4 | semidirect |
| 15. C131⋊#95 | C22 | semidirect |
| 19. C22⋊C8×C131 | C22 | semidirect |
| 23. C2×D524 | C2×C4 | semidirect |
| 34. C4⋊Dic131 | C2×C4 | semidirect |
| 106. C2×C131 | #327 | semidirect |
| 111. C131 | C2×#327 | semidirect |
| 114. C2×C22⋊C8 | D131 | semidirect |
| 129. C22⋊C8 | C2×D131 | semidirect |
| 219. C2 | #22553047 | 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 |
| C2×C131⋊#95 | 2 |
| #22553047 | 2 |
| C2×C22⋊C8×C131 | 2 |
| C2×#327 | 131 |