Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
616 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 1. C22×C8×D131 | C2 | semidirect |
| 2. C2×#16862217 | C2 | semidirect |
| 3. #22553545 | C2 | direct (N × H) |
| 4. C2×#16862180 | C2 | semidirect |
| 5. C2×#16862167 | C2 | semidirect |
| 6. C22×D8×C131 | C2 | semidirect |
| 11. C2×C8×D131 | C22 | semidirect |
| 13. #16862217 | C22 | semidirect |
| 16. #16862180 | C22 | semidirect |
| 17. #16862167 | C22 | semidirect |
| 20. C2×D8×C131 | C22 | semidirect |
| 44. C2×C8×C131 | D4 | semidirect |
| 48. C22×D131 | D8 | semidirect |
| 71. C8×C131 | C2×D4 | semidirect |
| 83. C2×D131 | C2×D8 | semidirect |
| 90. C2×C131 | #466 | semidirect |
| 95. C131 | C2×#466 | semidirect |
| 97. C22×D8 | D131 | semidirect |
| 107. C2×D8 | C2×D131 | semidirect |
| 137. C2×C8 | C22⋊D131 | semidirect |
| 167. C8 | C2×C22⋊D131 | semidirect |
| 187. C2 | #22553545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D131 | 2 |
| C2×#16862217 | 2 |
| #22553545 | 2 |
| C2×#16862180 | 2 |
| C2×#16862167 | 2 |
| C22×D8×C131 | 2 |
| C2×#466 | 131 |