Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 605 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. C23×C4×D131 | C2 | semidirect |
| 3. C2×#16862231 | C2 | direct (N × H) |
| 4. C22×Dic131⋊C4 | C2 | semidirect |
| 5. C22×(C2×D131)⋊C4 | C2 | semidirect |
| 6. C22×(C2×D131)⋊C4 | C2 | semidirect |
| 7. C22×(C2×D131)⋊C4 | C2 | semidirect |
| 8. C22×C4⋊C4×C131 | C2 | semidirect |
| 16. C22×C4×D131 | C22 | semidirect |
| 17. #16862231 | C22 | direct (N × H) |
| 18. C2×Dic131⋊C4 | C22 | semidirect |
| 19. C2×(C2×D131)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D131)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D131)⋊C4 | C22 | semidirect |
| 25. C2×C4⋊C4×C131 | C22 | semidirect |
| 41. C2×C4×D131 | C23 | semidirect |
| 42. Dic131⋊C4 | C23 | semidirect |
| 43. (C2×D131)⋊C4 | C23 | semidirect |
| 44. (C2×D131)⋊C4 | C23 | semidirect |
| 45. (C2×D131)⋊C4 | C23 | semidirect |
| 53. C4⋊C4×C131 | C23 | semidirect |
| 80. C22×C131 | #123 | semidirect |
| 98. C2×C131 | C2×#123 | semidirect |
| 104. C131 | C22×#123 | semidirect |
| 110. C22×C4⋊C4 | D131 | semidirect |
| 127. C2×C4⋊C4 | C2×D131 | semidirect |
| 155. C4⋊C4 | C22×D131 | semidirect |
| 193. C22 | #16862231 | direct (N × H) |
| 205. C2 | C2×#16862231 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D524 | 2 |
| C23×C4×D131 | 2 |
| C2×#16862231 | 2 |
| C22×Dic131⋊C4 | 2 |
| C22×(C2×D131)⋊C4 | 2 |
| C22×C4⋊C4×C131 | 2 |
| C22×#123 | 131 |