Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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×#16862190 | C2 | semidirect |
| 2. #22553695 | C2 | semidirect |
| 3. D8×Dic131 | C2 | semidirect |
| 4. Dic131⋊C16 | C2 | semidirect |
| 5. #22553117 | C2 | semidirect |
| 6. #22553113 | C2 | semidirect |
| 76. C131 | #2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862190 | 2 |
| #22553695 | 2 |
| D8×Dic131 | 2 |
| Dic131⋊C16 | 2 |
| #22553117 | 2 |
| #22553113 | 2 |
| C2×D16×C131 | 2 |
| #2210 | 131 |