Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 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 |
|---|---|---|
| 1. C22×#14523513 | C2 | semidirect |
| 2. C2×#16862274 | C2 | semidirect |
| 3. C2×#16862220 | C2 | semidirect |
| 4. #22553459 | C2 | semidirect |
| 5. #22553453 | C2 | semidirect |
| 6. #22553448 | C2 | semidirect |
| 7. #22553314 | C2 | semidirect |
| 8. #407×C131 | C2 | semidirect |
| 13. C2×#14523513 | C22 | semidirect |
| 14. C22×Dic262 | C22 | semidirect |
| 15. C22×D524 | C22 | semidirect |
| 16. C22×D524 | C22 | semidirect |
| 21. C2×#14523502 | C22 | semidirect |
| 22. C2×D1048 | C22 | semidirect |
| 26. #16862220 | C22 | semidirect |
| 27. C2×C4⋊Dic131 | C22 | semidirect |
| 29. #16862171 | C22 | semidirect |
| 30. #16862168 | C22 | semidirect |
| 32. C2×M16×C131 | C22 | semidirect |
| 33. C22⋊C8×C131 | C22 | semidirect |
| 34. C22⋊C8×C131 | C22 | semidirect |
| 42. #14523513 | D4 | semidirect |
| 89. Dic262 | C2×D4 | semidirect |
| 94. D524 | C2×D4 | semidirect |
| 131. C22×C131 | AGL(1,ℤ/8) | semidirect |
| 155. C131 | #3006 | semidirect |
| 164. #407 | D131 | semidirect |
| 180. C2×M16 | C2×D131 | semidirect |
| 189. C22⋊C8 | C2×D131 | semidirect |
| 190. C22⋊C8 | C2×D131 | semidirect |
| 295. C22 | #16862274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523513 | 2 |
| C2×#16862274 | 2 |
| C2×#16862220 | 2 |
| #22553459 | 2 |
| #22553453 | 2 |
| #22553448 | 2 |
| #22553314 | 2 |
| #407×C131 | 2 |
| #3006 | 131 |