Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
548 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 169 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×#16862238 | C2 | semidirect |
| 2. #22553235 | C2 | semidirect |
| 5. #22553185 | C2 | semidirect |
| 6. #22553181 | C2 | semidirect |
| 7. #22553177 | C2 | semidirect |
| 8. C4×C4⋊Dic131 | C2 | semidirect |
| 107. C131 | #2566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862238 | 2 |
| #22553235 | 2 |
| #22553215 | 2 |
| #22553185 | 2 |
| #22553181 | 2 |
| #22553177 | 2 |
| C4×C4⋊Dic131 | 2 |
| C2×C4×D4×C131 | 2 |
| #2566 | 131 |