Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#16862177 | C2 | semidirect |
| 3. C2×#16862170 | C2 | semidirect |
| 5. C2×C4×C131⋊C8 | C2 | semidirect |
| 7. #391×C131 | C2 | semidirect |
| 11. C2×#14523500 | C4 | semidirect |
| 68. C131⋊C8 | C22⋊C4 | semidirect |
| 81. C2×C4×C131 | SD16 | semidirect |
| 112. C131 | #1968 | semidirect |
| 119. #391 | D131 | semidirect |
| 192. C2×C4 | #14523500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523500 | 2 |
| C2×#16862177 | 2 |
| C2×#16862170 | 2 |
| C2×#16862166 | 2 |
| C2×C4×C131⋊C8 | 2 |
| #22553214 | 2 |
| #391×C131 | 2 |
| #1968 | 131 |