Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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×#16862253 | C2 | semidirect |
| 3. #22553320 | C2 | semidirect |
| 4. #22553311 | C2 | semidirect |
| 5. #22553306 | C2 | semidirect |
| 6. C2×#16862169 | C2 | semidirect |
| 7. #520×C131 | C2 | semidirect |
| 9. #16862293 | C4 | semidirect |
| 28. #14523513 | C2×C4 | semidirect |
| 32. C2×Dic262 | C2×C4 | semidirect |
| 94. C131 | #2898 | semidirect |
| 98. #520 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862293 | 2 |
| C2×#16862253 | 2 |
| #22553320 | 2 |
| #22553311 | 2 |
| #22553306 | 2 |
| C2×#16862169 | 2 |
| #520×C131 | 2 |
| #2898 | 131 |