Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
196 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22553088 | C2 | semidirect |
| 3. C4×C131⋊C16 | C2 | semidirect |
| 5. #16862186 | C4 | direct (N × H) |
| 14. C131⋊C16 | C2×C4 | semidirect |
| 43. C4×C131 | M32 | semidirect |
| 49. C131 | C4×M32 | semidirect |
| 93. C4 | #16862186 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862186 | 2 |
| #22553088 | 2 |
| C4×C131⋊C16 | 2 |
| C2×C4×C8×C131 | 2 |
| C4×M32 | 131 |