Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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×#16862277 | C2 | semidirect |
| 3. C2×#16862277 | C2 | semidirect |
| 4. #22554078 | C2 | semidirect |
| 5. #22553586 | C2 | semidirect |
| 6. #22553578 | C2 | semidirect |
| 7. #22553360 | C2 | semidirect |
| 8. #22553294 | C2 | semidirect |
| 9. C2×#101×C131 | C2 | semidirect |
| 22. C2×#14523503 | C22 | semidirect |
| 24. C2×#14523500 | C22 | semidirect |
| 30. #16862181 | C22 | semidirect |
| 31. #16862164 | C22 | semidirect |
| 32. #16862162 | C22 | semidirect |
| 36. #101×C131 | C22 | semidirect |
| 142. C131 | #3069 | semidirect |
| 152. C2×#101 | D131 | semidirect |
| 178. #101 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554112 | 2 |
| C2×#16862277 | 2 |
| #22554078 | 2 |
| #22553586 | 2 |
| #22553578 | 2 |
| #22553360 | 2 |
| #22553294 | 2 |
| C2×#101×C131 | 2 |
| #3069 | 131 |