Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #22553270 | C2 | semidirect |
| 4. C2×#16862157 | C2 | semidirect |
| 5. #22553076 | C2 | semidirect |
| 6. #22553072 | C2 | semidirect |
| 9. #16862253 | C4 | semidirect |
| 16. #16862170 | C4 | semidirect |
| 17. #16862167 | C4 | semidirect |
| 24. #104×C131 | C4 | semidirect |
| 98. C131 | #1765 | semidirect |
| 118. #104 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862253 | 2 |
| #22553308 | 2 |
| #22553270 | 2 |
| C2×#16862157 | 2 |
| #22553076 | 2 |
| #22553072 | 2 |
| C2×#104×C131 | 2 |
| #1765 | 131 |