Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
4632 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1157 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×D167 | C2 | semidirect |
| 3. C22×C22⋊Dic167 | C2 | semidirect |
| 4. C22×(C2×D167)⋊C4 | C2 | semidirect |
| 5. C2×C22⋊C4×D167 | C2 | direct (N × H) |
| 6. C22×C22⋊C4×C167 | C2 | semidirect |
| 8. C24×D167 | C4 | semidirect |
| 12. C23×Dic167 | C22 | semidirect |
| 14. C22×C4×D167 | C22 | semidirect |
| 15. C2×C22⋊Dic167 | C22 | semidirect |
| 16. C2×(C2×D167)⋊C4 | C22 | semidirect |
| 17. C22⋊C4×D167 | C22 | direct (N × H) |
| 19. C23×C4×C167 | C22 | semidirect |
| 20. C2×C22⋊C4×C167 | C22 | semidirect |
| 25. C23×D167 | C2×C4 | semidirect |
| 26. C23×D167 | C2×C4 | semidirect |
| 32. C22×Dic167 | C23 | semidirect |
| 34. C2×C4×D167 | C23 | semidirect |
| 35. C22⋊Dic167 | C23 | semidirect |
| 36. (C2×D167)⋊C4 | C23 | semidirect |
| 38. C24×C167 | C2×C4 | semidirect |
| 42. C22×C4×C167 | C23 | semidirect |
| 43. C22⋊C4×C167 | C23 | semidirect |
| 48. C22×D167 | C22⋊C4 | direct (N × H) |
| 50. C22×D167 | C22×C4 | semidirect |
| 51. C22×D167 | C22×C4 | semidirect |
| 56. C2×Dic167 | C24 | semidirect |
| 61. C23×C167 | C22×C4 | semidirect |
| 66. C2×C4×C167 | C24 | semidirect |
| 69. C22×C167 | C2×C22⋊C4 | semidirect |
| 71. C22×C167 | C23×C4 | semidirect |
| 77. C2×D167 | C2×C22⋊C4 | direct (N × H) |
| 79. C2×D167 | C23×C4 | semidirect |
| 84. C2×C167 | C22×C22⋊C4 | semidirect |
| 88. D167 | C22×C22⋊C4 | direct (N × H) |
| 89. C167 | C23×C22⋊C4 | semidirect |
| 96. C22×C22⋊C4 | D167 | direct (N × H) |
| 106. C23×C4 | C2×D167 | semidirect |
| 110. C2×C22⋊C4 | C2×D167 | direct (N × H) |
| 122. C24 | C4×D167 | semidirect |
| 130. C22×C4 | C22×D167 | semidirect |
| 133. C22⋊C4 | C22×D167 | direct (N × H) |
| 148. C23 | C2×C4×D167 | semidirect |
| 156. C2×C4 | C23×D167 | semidirect |
| 166. C22 | C22⋊C4×D167 | direct (N × H) |
| 168. C22 | C22×C4×D167 | semidirect |
| 176. C2 | C2×C22⋊C4×D167 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D167 | 2 |
| C23×C4×D167 | 2 |
| C22×C22⋊Dic167 | 2 |
| C22×(C2×D167)⋊C4 | 2 |
| C2×C22⋊C4×D167 | 2 |
| C22×C22⋊C4×C167 | 2 |
| C23×C22⋊C4 | 167 |