Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
584 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 161 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. #22553250 | C2 | semidirect |
| 3. #22553247 | C2 | semidirect |
| 4. #22553231 | C2 | semidirect |
| 5. #22553223 | C2 | semidirect |
| 6. #22553193 | C2 | semidirect |
| 8. #22553183 | C2 | semidirect |
| 9. #22553170 | C2 | semidirect |
| 10. C2×C131⋊#95 | C2 | semidirect |
| 11. C2×C22⋊Q8×C131 | C2 | semidirect |
| 40. C2×C22⋊D131 | Q8 | semidirect |
| 141. C131 | #2564 | semidirect |
| 143. C2×C22⋊Q8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D131 | 2 |
| #22553250 | 2 |
| #22553247 | 2 |
| #22553231 | 2 |
| #22553223 | 2 |
| #22553193 | 2 |
| #22553189 | 2 |
| #22553183 | 2 |
| #22553170 | 2 |
| C2×C131⋊#95 | 2 |
| C2×C22⋊Q8×C131 | 2 |
| #2564 | 131 |