Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic262 | C2 | semidirect |
| 3. #22553412 | C2 | direct (N × H) |
| 4. C2×#16862179 | C2 | semidirect |
| 5. C2×#16862169 | C2 | semidirect |
| 7. C2×#16862157 | C2 | semidirect |
| 10. C2×#14523501 | C4 | semidirect |
| 15. C4×Dic262 | C22 | semidirect |
| 19. #16862179 | C22 | semidirect |
| 20. #16862169 | C22 | semidirect |
| 22. #16862157 | C22 | semidirect |
| 32. C2×Dic262 | C2×C4 | semidirect |
| 36. #14523501 | C2×C4 | semidirect |
| 38. C2×C131⋊C8 | C2×C4 | semidirect |
| 63. Dic262 | C22×C4 | semidirect |
| 69. C131⋊C8 | C22×C4 | semidirect |
| 106. C2×C131 | #440 | semidirect |
| 110. C131 | C2×#440 | semidirect |
| 217. C2 | #22553412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523501 | 2 |
| C2×C4×Dic262 | 2 |
| #22553412 | 2 |
| C2×#16862179 | 2 |
| C2×#16862169 | 2 |
| C2×#16862167 | 2 |
| C2×#16862157 | 2 |
| C2×C4×D4×C131 | 2 |
| C2×#440 | 131 |