Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
280 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553044 | C2 | direct (N × H) |
| 22. C2×Dic262 | C8 | semidirect |
| 45. Dic262 | C2×C8 | semidirect |
| 78. C2×C131 | Q8⋊C8 | semidirect |
| 82. C131 | C2×Q8⋊C8 | semidirect |
| 161. C2 | #22553044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic262 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| #22553044 | 2 |
| C2×C4×C8×C131 | 2 |
| C2×Q8⋊C8 | 131 |