Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 4. #22553606 | C2 | semidirect |
| 5. #22553521 | C2 | semidirect |
| 8. #22553406 | C2 | semidirect |
| 9. #22553404 | C2 | semidirect |
| 91. C2×Dic131 | Q16 | semidirect |
| 127. C131 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553864 | 2 |
| C2×#16862211 | 2 |
| #22553647 | 2 |
| #22553606 | 2 |
| #22553521 | 2 |
| #22553470 | 2 |
| #22553467 | 2 |
| #22553406 | 2 |
| #22553404 | 2 |
| #22553362 | 2 |
| #484×C131 | 2 |
| #3104 | 131 |