Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×#16862254 | C2 | semidirect |
| 3. #22553886 | C2 | semidirect |
| 4. #22553567 | C2 | semidirect |
| 5. #22553555 | C2 | semidirect |
| 6. #22553550 | C2 | semidirect |
| 7. #22553538 | C2 | semidirect |
| 8. #22553354 | C2 | semidirect |
| 9. #22553308 | C2 | semidirect |
| 10. C2×#16862170 | C2 | semidirect |
| 11. C2×#137×C131 | C2 | semidirect |
| 83. M16×C131 | D4 | semidirect |
| 143. C131 | #3063 | semidirect |
| 145. C2×#137 | D131 | semidirect |
| 210. M16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862254 | 2 |
| #22553890 | 2 |
| #22553886 | 2 |
| #22553567 | 2 |
| #22553555 | 2 |
| #22553550 | 2 |
| #22553538 | 2 |
| #22553354 | 2 |
| #22553308 | 2 |
| C2×#16862170 | 2 |
| C2×#137×C131 | 2 |
| #3063 | 131 |