Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862235 | C2 | semidirect |
| 3. #41×Dic131 | C2 | semidirect |
| 4. #22553536 | C2 | semidirect |
| 5. #22553529 | C2 | semidirect |
| 6. #22553335 | C2 | semidirect |
| 7. #22553321 | C2 | semidirect |
| 8. #22553318 | C2 | semidirect |
| 9. C2×#137×C131 | C2 | semidirect |
| 18. Q8×Dic131 | C22 | semidirect |
| 20. D4×Dic131 | C22 | semidirect |
| 26. Dic131⋊C8 | C22 | semidirect |
| 27. #16862170 | C22 | semidirect |
| 32. C2×Q16×C131 | C22 | semidirect |
| 33. C2×SD16×C131 | C22 | semidirect |
| 125. C131 | #3040 | semidirect |
| 127. C2×#137 | D131 | semidirect |
| 141. C2×Q16 | C2×D131 | semidirect |
| 143. C2×SD16 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C2×#16862235 | 2 |
| #41×Dic131 | 2 |
| #22553536 | 2 |
| #22553529 | 2 |
| #22553335 | 2 |
| #22553321 | 2 |
| #22553318 | 2 |
| C2×#137×C131 | 2 |
| #3040 | 131 |