Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#16862211 | C2 | semidirect |
| 3. #22553647 | C2 | semidirect |
| 4. #22553622 | C2 | semidirect |
| 5. #22553533 | C2 | semidirect |
| 6. #22553470 | C2 | semidirect |
| 8. #22553418 | C2 | semidirect |
| 9. #22553409 | C2 | semidirect |
| 10. #22553366 | C2 | semidirect |
| 131. C131 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553843 | 2 |
| C2×#16862211 | 2 |
| #22553647 | 2 |
| #22553622 | 2 |
| #22553533 | 2 |
| #22553470 | 2 |
| #22553450 | 2 |
| #22553418 | 2 |
| #22553409 | 2 |
| #22553366 | 2 |
| #481×C131 | 2 |
| #3117 | 131 |