Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
448 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. C22×#14523503 | C2 | semidirect |
| 5. #22553586 | C2 | direct (N × H) |
| 6. C2×#16862181 | C2 | semidirect |
| 7. C2×#16862164 | C2 | semidirect |
| 8. C2×#101×C131 | C2 | semidirect |
| 20. C2×#14523503 | C22 | semidirect |
| 29. #16862181 | C22 | semidirect |
| 30. #16862164 | C22 | semidirect |
| 34. #101×C131 | C22 | semidirect |
| 130. C2×C131 | #473 | semidirect |
| 133. C131 | C2×#473 | semidirect |
| 142. C2×#101 | D131 | semidirect |
| 168. #101 | C2×D131 | semidirect |
| 265. C2 | #22553586 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862279 | 2 |
| C2×#16862277 | 2 |
| C22×#14523503 | 2 |
| C2×#16862254 | 2 |
| #22553586 | 2 |
| C2×#16862181 | 2 |
| C2×#16862164 | 2 |
| C2×#101×C131 | 2 |
| C2×#473 | 131 |