Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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×C4⋊(C131⋊C8) | C2 | semidirect |
| 3. C2×Dic131⋊C8 | C2 | semidirect |
| 6. #22553066 | C2 | semidirect |
| 7. #336×C131 | C2 | semidirect |
| 72. C2×Dic131 | M16 | semidirect |
| 85. C2×C4×C131 | M16 | semidirect |
| 125. C131 | #1851 | semidirect |
| 133. #336 | D131 | semidirect |
| 209. C2×C4 | #14523496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523496 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| C2×Dic131⋊C8 | 2 |
| C2×(C2×D131)⋊C8 | 2 |
| C4×(C2×D131)⋊C4 | 2 |
| #22553066 | 2 |
| #336×C131 | 2 |
| #1851 | 131 |