Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14523500 | C2 | semidirect |
| 2. C22×#14523496 | C2 | semidirect |
| 3. C2×#16862222 | C2 | semidirect |
| 5. #22553561 | C2 | direct (N × H) |
| 6. C2×#16862179 | C2 | semidirect |
| 7. C2×#16862168 | C2 | semidirect |
| 8. C2×#103×C131 | C2 | semidirect |
| 13. C2×#14523500 | C22 | semidirect |
| 15. C2×#14523496 | C22 | semidirect |
| 18. #16862222 | C22 | semidirect |
| 25. #16862179 | C22 | semidirect |
| 26. #16862168 | C22 | semidirect |
| 30. #103×C131 | C22 | semidirect |
| 47. C2×C131⋊C8 | D4 | semidirect |
| 84. C131⋊C8 | C2×D4 | semidirect |
| 117. C2×C131 | #468 | semidirect |
| 123. C131 | C2×#468 | semidirect |
| 131. C2×#103 | D131 | semidirect |
| 153. #103 | C2×D131 | semidirect |
| 243. C2 | #22553561 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523500 | 2 |
| C22×#14523496 | 2 |
| C2×#16862222 | 2 |
| C2×#16862221 | 2 |
| #22553561 | 2 |
| C2×#16862179 | 2 |
| C2×#16862168 | 2 |
| C2×#103×C131 | 2 |
| C2×#468 | 131 |