Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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×Q8×Dic131 | C2 | semidirect |
| 4. #22553397 | C2 | direct (N × H) |
| 5. C2×#16862177 | C2 | semidirect |
| 7. C2×C8×Dic131 | C2 | semidirect |
| 8. C2×#103×C131 | C2 | semidirect |
| 11. C2×#14523500 | C4 | semidirect |
| 15. Q8×Dic131 | C22 | semidirect |
| 23. #16862177 | C22 | semidirect |
| 25. C8×Dic131 | C22 | semidirect |
| 29. #103×C131 | C22 | semidirect |
| 40. #14523500 | C2×C4 | semidirect |
| 41. C2×C131⋊C8 | C2×C4 | semidirect |
| 52. C2×Q8×C131 | C2×C4 | semidirect |
| 71. C2×Dic131 | SD16 | semidirect |
| 75. C131⋊C8 | C22×C4 | semidirect |
| 79. Q8×C131 | C22×C4 | semidirect |
| 104. Dic131 | C2×SD16 | semidirect |
| 105. C2×C131 | C4×SD16 | semidirect |
| 110. C131 | C2×C4×SD16 | semidirect |
| 117. C2×#103 | D131 | semidirect |
| 138. #103 | C2×D131 | semidirect |
| 144. C2×Q8 | C4×D131 | semidirect |
| 179. Q8 | C2×C4×D131 | semidirect |
| 217. C2 | #22553397 | 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 |
| C2×Q8×Dic131 | 2 |
| C2×#16862208 | 2 |
| #22553397 | 2 |
| C2×#16862177 | 2 |
| C2×#16862168 | 2 |
| C2×C8×Dic131 | 2 |
| C2×#103×C131 | 2 |
| C2×C4×SD16 | 131 |