Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
544 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 185 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. #22553244 | C2 | semidirect |
| 3. #22553233 | C2 | semidirect |
| 4. #22553218 | C2 | semidirect |
| 5. #22553210 | C2 | semidirect |
| 51. C22×C4×C131 | Q8 | semidirect |
| 57. C22⋊C4×C131 | Q8 | semidirect |
| 114. C131 | #2549 | semidirect |
| 159. C22×C4 | Dic262 | semidirect |
| 172. C22⋊C4 | Dic262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862223 | 2 |
| #22553244 | 2 |
| #22553233 | 2 |
| #22553218 | 2 |
| #22553210 | 2 |
| #22553187 | 2 |
| #22553172 | 2 |
| C2×C131⋊#95 | 2 |
| C4×C22⋊C4×C131 | 2 |
| #2549 | 131 |