Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
334 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #22553276 | C2 | semidirect |
| 2. C2×C131⋊#95 | C2 | semidirect |
| 3. #22553049 | C2 | semidirect |
| 4. #22553046 | C2 | semidirect |
| 12. C2×#41×C131 | C4 | semidirect |
| 15. C22⋊Q8×C131 | C4 | semidirect |
| 17. #121×C131 | C4 | semidirect |
| 22. #117×C131 | C4 | semidirect |
| 31. C2×Q8×C131 | C2×C4 | semidirect |
| 35. C2×D4×C131 | C2×C4 | semidirect |
| 46. C4⋊C4×C131 | C2×C4 | semidirect |
| 47. C4⋊C4×C131 | C2×C4 | semidirect |
| 119. C131 | #1504 | semidirect |
| 126. C2×#41 | Dic131 | semidirect |
| 131. C22⋊Q8 | Dic131 | semidirect |
| 133. #121 | Dic131 | semidirect |
| 138. #117 | Dic131 | semidirect |
| 145. C2×Q8 | C2×Dic131 | semidirect |
| 149. C2×D4 | C2×Dic131 | semidirect |
| 166. C4⋊C4 | C2×Dic131 | semidirect |
| 167. C4⋊C4 | C2×Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553276 | 2 |
| C2×C131⋊#95 | 2 |
| #22553049 | 2 |
| #22553046 | 2 |
| #525×C131 | 2 |
| #1504 | 131 |