Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
4544 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 725 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. C25×D131 | C2 | semidirect |
| 2. C23×D524 | C2 | semidirect |
| 3. C23×C22⋊D131 | C2 | semidirect |
| 4. C2×#16862216 | C2 | direct (N × H) |
| 5. C22×(C2×D131)⋊C4 | C2 | semidirect |
| 6. C22×C22⋊C4×C131 | C2 | semidirect |
| 10. C24×D131 | C22 | semidirect |
| 11. C24×D131 | C22 | semidirect |
| 13. C22×D524 | C22 | semidirect |
| 15. C22×C22⋊D131 | C22 | semidirect |
| 16. C23×Dic131 | C22 | semidirect |
| 17. #16862216 | C22 | direct (N × H) |
| 18. C2×(C2×D131)⋊C4 | C22 | semidirect |
| 20. C23×C4×C131 | C22 | semidirect |
| 21. C2×C22⋊C4×C131 | C22 | semidirect |
| 29. C23×D131 | D4 | semidirect |
| 31. C23×D131 | C23 | semidirect |
| 32. C23×D131 | C23 | semidirect |
| 34. C2×D524 | C23 | semidirect |
| 36. C2×C22⋊D131 | C23 | semidirect |
| 38. C22×Dic131 | C23 | semidirect |
| 39. (C2×D131)⋊C4 | C23 | semidirect |
| 41. C24×C131 | D4 | semidirect |
| 45. C22×C4×C131 | C23 | semidirect |
| 46. C22⋊C4×C131 | C23 | semidirect |
| 56. C22×D131 | C2×D4 | semidirect |
| 58. C22×D131 | C24 | semidirect |
| 62. C2×Dic131 | C24 | semidirect |
| 67. C23×C131 | C2×D4 | semidirect |
| 71. C2×C4×C131 | C24 | semidirect |
| 74. C22×C131 | #120 | semidirect |
| 77. C22×C131 | C22×D4 | semidirect |
| 86. C2×D131 | C22×D4 | semidirect |
| 90. C2×C131 | C2×#120 | semidirect |
| 95. C131 | C22×#120 | semidirect |
| 102. C22×C22⋊C4 | D131 | semidirect |
| 114. C23×C4 | C2×D131 | semidirect |
| 117. C2×C22⋊C4 | C2×D131 | semidirect |
| 130. C24 | D524 | semidirect |
| 140. C22×C4 | C22×D131 | semidirect |
| 142. C22⋊C4 | C22×D131 | semidirect |
| 159. C23 | C2×D524 | semidirect |
| 167. C2×C4 | C23×D131 | semidirect |
| 178. C22 | #16862216 | direct (N × H) |
| 181. C22 | C22×D524 | semidirect |
| 188. C2 | C2×#16862216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D131 | 2 |
| C23×D524 | 2 |
| C23×C22⋊D131 | 2 |
| C2×#16862216 | 2 |
| C22×(C2×D131)⋊C4 | 2 |
| C22×C22⋊C4×C131 | 2 |
| C22×#120 | 131 |