Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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. #22553238 | C2 | semidirect |
| 3. #22553223 | C2 | semidirect |
| 4. #22553202 | C2 | semidirect |
| 5. #22553173 | C2 | semidirect |
| 7. C4×C22⋊Dic131 | C2 | semidirect |
| 8. C2×C22⋊Q8×C131 | C2 | semidirect |
| 17. C2×C4×Dic131 | C22 | semidirect |
| 18. C131⋊#95 | C22 | semidirect |
| 19. C131⋊#95 | C22 | semidirect |
| 20. C131⋊#95 | C22 | semidirect |
| 21. C22×Q8×C131 | C22 | semidirect |
| 24. C2×C4⋊C4×C131 | C22 | semidirect |
| 25. C2×C4⋊C4×C131 | C22 | semidirect |
| 110. C131 | #2561 | semidirect |
| 112. C2×C22⋊Q8 | D131 | semidirect |
| 121. C22×Q8 | C2×D131 | semidirect |
| 125. C2×C4⋊C4 | C2×D131 | semidirect |
| 126. 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 |
|---|---|
| C22×(C2×D131)⋊C4 | 2 |
| #22553238 | 2 |
| #22553223 | 2 |
| #22553202 | 2 |
| #22553173 | 2 |
| #22553167 | 2 |
| C4×C22⋊Dic131 | 2 |
| C2×C22⋊Q8×C131 | 2 |
| #2561 | 131 |