Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22553636 | C2 | semidirect |
| 3. #22553630 | C2 | semidirect |
| 4. #22553625 | C2 | semidirect |
| 5. #22553355 | C2 | semidirect |
| 6. #22553316 | C2 | semidirect |
| 7. #22553276 | C2 | semidirect |
| 8. C2×#117×C131 | C2 | semidirect |
| 18. #16862179 | C22 | semidirect |
| 19. #16862177 | C22 | semidirect |
| 20. #16862166 | C22 | semidirect |
| 21. #16862166 | C22 | semidirect |
| 22. C22⋊(C131⋊C8) | C22 | semidirect |
| 23. C22⋊(C131⋊C8) | C22 | semidirect |
| 28. #117×C131 | C22 | semidirect |
| 29. C2×C4⋊C4×C131 | C22 | semidirect |
| 30. C2×C4⋊C4×C131 | C22 | semidirect |
| 125. C131 | #3094 | semidirect |
| 128. C2×#117 | D131 | semidirect |
| 146. #117 | C2×D131 | semidirect |
| 148. C2×C4⋊C4 | C2×D131 | semidirect |
| 149. C2×C4⋊C4 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862220 | 2 |
| #22553636 | 2 |
| #22553630 | 2 |
| #22553625 | 2 |
| #22553355 | 2 |
| #22553316 | 2 |
| #22553276 | 2 |
| C2×#117×C131 | 2 |
| #3094 | 131 |