Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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. C2×#16862202 | C2 | semidirect |
| 3. #22553175 | C2 | semidirect |
| 4. #22553171 | C2 | semidirect |
| 6. #22553159 | C2 | semidirect |
| 7. #381×C131 | C2 | semidirect |
| 11. C22×C4×D131 | C4 | semidirect |
| 15. C2×Dic131⋊C4 | C22 | semidirect |
| 18. C2×C4×Dic131 | C22 | semidirect |
| 19. C131⋊#95 | C22 | semidirect |
| 22. #95×C131 | C22 | semidirect |
| 56. C2×Dic131 | C22⋊C4 | semidirect |
| 82. C2×D131 | #117 | semidirect |
| 93. C131 | #2280 | semidirect |
| 98. #381 | D131 | semidirect |
| 116. #95 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D131 | 2 |
| C2×#16862202 | 2 |
| #22553175 | 2 |
| #22553171 | 2 |
| #22553167 | 2 |
| #22553159 | 2 |
| #381×C131 | 2 |
| #2280 | 131 |