Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22553649 | C2 | direct (N × H) |
| 4. C2×#16862179 | C2 | semidirect |
| 5. C2×#16862171 | C2 | semidirect |
| 6. C2×#16862169 | C2 | semidirect |
| 8. C2×#107×C131 | C2 | semidirect |
| 21. #16862179 | C22 | semidirect |
| 22. #16862171 | C22 | semidirect |
| 23. #16862169 | C22 | semidirect |
| 28. #107×C131 | C22 | semidirect |
| 103. C2×C131 | #484 | semidirect |
| 108. C131 | C2×#484 | semidirect |
| 114. C2×#107 | D131 | semidirect |
| 134. #107 | C2×D131 | semidirect |
| 213. C2 | #22553649 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862226 | 2 |
| C2×C4⋊C4×D131 | 2 |
| #22553649 | 2 |
| C2×#16862179 | 2 |
| C2×#16862171 | 2 |
| C2×#16862169 | 2 |
| C2×(C2×D131)⋊C8 | 2 |
| C2×#107×C131 | 2 |
| C2×#484 | 131 |