Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#16862244 | C2 | semidirect |
| 5. #22553521 | C2 | semidirect |
| 6. #22553516 | C2 | semidirect |
| 7. #22553335 | C2 | semidirect |
| 8. #22553320 | C2 | semidirect |
| 9. #419×C131 | C2 | semidirect |
| 116. Dic131 | #137 | semidirect |
| 121. C131 | #3039 | semidirect |
| 131. #419 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862279 | 2 |
| C2×#16862277 | 2 |
| C2×#16862244 | 2 |
| #22553780 | 2 |
| #22553521 | 2 |
| #22553516 | 2 |
| #22553335 | 2 |
| #22553320 | 2 |
| #419×C131 | 2 |
| #3039 | 131 |