Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22553666 | C2 | direct (N × H) |
| 3. C2×#16862170 | C2 | semidirect |
| 5. C2×C4×C131⋊C8 | C2 | semidirect |
| 9. #16862238 | C22 | semidirect |
| 12. #16862170 | C22 | semidirect |
| 14. C4×C131⋊C8 | C22 | semidirect |
| 70. C2×C131 | #488 | semidirect |
| 73. C131 | C2×#488 | semidirect |
| 144. C2 | #22553666 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862238 | 2 |
| #22553666 | 2 |
| C2×#16862170 | 2 |
| C2×#16862167 | 2 |
| C2×C4×C131⋊C8 | 2 |
| C2×#124×C131 | 2 |
| C2×#488 | 131 |