Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22553037 | C2 | direct (N × H) |
| 26. C22×Dic131 | C8 | semidirect |
| 53. C2×Dic131 | C2×C8 | semidirect |
| 95. C2×C131 | #324 | semidirect |
| 99. C131 | C2×#324 | semidirect |
| 195. C2 | #22553037 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic131⋊C4 | 2 |
| C2×C22⋊(C131⋊C8) | 2 |
| #22553037 | 2 |
| C2×C22⋊C8×C131 | 2 |
| C2×#324 | 131 |