Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16862181 | C2 | semidirect |
| 5. #22553071 | C2 | semidirect |
| 6. #22553066 | C2 | semidirect |
| 7. #424×C131 | C2 | semidirect |
| 18. #16862169 | C4 | semidirect |
| 19. #16862169 | C4 | semidirect |
| 20. #16862166 | C4 | semidirect |
| 21. #16862166 | C4 | semidirect |
| 109. C131 | #1866 | semidirect |
| 113. #424 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862252 | 2 |
| C2×#16862181 | 2 |
| C2×#16862172 | 2 |
| #22553306 | 2 |
| #22553071 | 2 |
| #22553066 | 2 |
| #424×C131 | 2 |
| #1866 | 131 |