Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#14523500 | C2 | semidirect |
| 3. #22553462 | C2 | direct (N × H) |
| 4. C2×#16862166 | C2 | semidirect |
| 5. C2×C22⋊(C131⋊C8) | C2 | semidirect |
| 6. C2×C22⋊Q8×C131 | C2 | semidirect |
| 14. C2×#14523500 | C22 | semidirect |
| 15. C22×C131⋊C8 | C22 | semidirect |
| 16. #16862166 | C22 | semidirect |
| 17. C22⋊(C131⋊C8) | C22 | semidirect |
| 18. C22×Q8×C131 | C22 | semidirect |
| 21. C22⋊Q8×C131 | C22 | semidirect |
| 23. C2×C4⋊C4×C131 | C22 | semidirect |
| 40. C2×C131⋊C8 | C23 | semidirect |
| 44. C2×Q8×C131 | C23 | semidirect |
| 54. C4⋊C4×C131 | C23 | semidirect |
| 71. C23×C131 | SD16 | semidirect |
| 92. C22×C131 | C2×SD16 | semidirect |
| 106. C2×C131 | #450 | semidirect |
| 111. C131 | C2×#450 | semidirect |
| 115. C2×C22⋊Q8 | D131 | semidirect |
| 120. C22×Q8 | C2×D131 | semidirect |
| 131. C22⋊Q8 | C2×D131 | semidirect |
| 133. C2×C4⋊C4 | C2×D131 | semidirect |
| 145. C2×Q8 | C22×D131 | semidirect |
| 166. C4⋊C4 | C22×D131 | semidirect |
| 178. C23 | #14523500 | semidirect |
| 209. C22 | C2×#14523500 | semidirect |
| 219. C2 | #22553462 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D524 | 2 |
| C22×#14523500 | 2 |
| #22553462 | 2 |
| C2×#16862166 | 2 |
| C2×C22⋊(C131⋊C8) | 2 |
| C2×C22⋊Q8×C131 | 2 |
| C2×#450 | 131 |