Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. C2×#16862191 | C2 | semidirect |
| 2. C2×#16862190 | C2 | semidirect |
| 3. C2×#16862187 | C2 | semidirect |
| 4. #22553695 | C2 | semidirect |
| 5. #22553687 | C2 | semidirect |
| 6. #22553087 | C2 | semidirect |
| 7. C2×D16×C131 | C2 | semidirect |
| 35. C131⋊C16 | D4 | semidirect |
| 43. C16×C131 | D4 | semidirect |
| 78. C131 | #2250 | semidirect |
| 83. C2×D16 | D131 | semidirect |
| 122. C16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862191 | 2 |
| C2×#16862190 | 2 |
| C2×#16862187 | 2 |
| #22553695 | 2 |
| #22553687 | 2 |
| #22553087 | 2 |
| C2×D16×C131 | 2 |
| #2250 | 131 |