Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
436 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16862168 | C2 | semidirect |
| 3. C2×#16862167 | C2 | semidirect |
| 4. C2×#16862166 | C2 | semidirect |
| 5. C2×C8×Dic131 | C2 | semidirect |
| 6. #22553181 | C2 | semidirect |
| 7. C2×#102×C131 | C2 | semidirect |
| 12. #16862242 | C4 | semidirect |
| 38. C2×C131⋊C8 | D4 | semidirect |
| 55. C2×C8×C131 | D4 | semidirect |
| 114. Dic131 | #102 | semidirect |
| 122. C131 | #1957 | semidirect |
| 128. C2×#102 | D131 | semidirect |
| 173. C2×C8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862242 | 2 |
| C2×#16862168 | 2 |
| C2×#16862167 | 2 |
| C2×#16862166 | 2 |
| C2×C8×Dic131 | 2 |
| #22553181 | 2 |
| C2×#102×C131 | 2 |
| #1957 | 131 |