Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14523501 | C2 | semidirect |
| 2. C22×C8×D131 | C2 | semidirect |
| 3. C2×#16862226 | C2 | semidirect |
| 5. #22553540 | C2 | direct (N × H) |
| 6. C2×#16862177 | C2 | semidirect |
| 7. C2×#16862171 | C2 | semidirect |
| 8. C2×#102×C131 | C2 | semidirect |
| 13. C2×#14523501 | C22 | semidirect |
| 16. C2×C8×D131 | C22 | semidirect |
| 18. #16862226 | C22 | semidirect |
| 25. #16862177 | C22 | semidirect |
| 26. #16862171 | C22 | semidirect |
| 30. #102×C131 | C22 | semidirect |
| 46. C2×C131⋊C8 | D4 | semidirect |
| 67. C22×D131 | SD16 | semidirect |
| 82. C131⋊C8 | C2×D4 | semidirect |
| 109. C2×D131 | C2×SD16 | semidirect |
| 118. C2×C131 | #465 | semidirect |
| 123. C131 | C2×#465 | semidirect |
| 132. C2×#102 | D131 | semidirect |
| 154. #102 | C2×D131 | semidirect |
| 243. C2 | #22553540 | 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 |
| C22×C8×D131 | 2 |
| C2×#16862226 | 2 |
| C2×#16862217 | 2 |
| #22553540 | 2 |
| C2×#16862177 | 2 |
| C2×#16862171 | 2 |
| C2×#102×C131 | 2 |
| C2×#465 | 131 |