Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#16862271 | C2 | semidirect |
| 2. C2×#16862243 | C2 | semidirect |
| 3. #22553702 | C2 | semidirect |
| 4. #22553688 | C2 | semidirect |
| 5. #22553686 | C2 | semidirect |
| 6. C4×#14523497 | C2 | semidirect |
| 7. #532×C131 | C2 | semidirect |
| 11. C2×#14523500 | C22 | semidirect |
| 12. C2×#14523498 | C22 | semidirect |
| 17. #16862157 | C22 | semidirect |
| 18. C4×C131⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C131 | C22 | semidirect |
| 21. #127×C131 | C22 | semidirect |
| 22. #124×C131 | C22 | semidirect |
| 35. #14523497 | D4 | semidirect |
| 57. C131⋊C8 | C2×D4 | semidirect |
| 83. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 90. C131 | #3151 | semidirect |
| 93. #532 | D131 | semidirect |
| 106. C4⋊Q8 | C2×D131 | semidirect |
| 110. #127 | C2×D131 | semidirect |
| 111. #124 | C2×D131 | semidirect |
| 174. C4 | #16862271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C2×#16862243 | 2 |
| #22553702 | 2 |
| #22553688 | 2 |
| #22553686 | 2 |
| C4×#14523497 | 2 |
| #532×C131 | 2 |
| #3151 | 131 |