Finite Group DatabasebetaFinite Group DatabasebetaOrder 32340.
208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D21⋊D55 |
| commutator, cosocle, hypocenter | C3×C5×C7×C11 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C11 | C22 |
| LCS | G ▷ C3×C5×C7×C11 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C7×D385 | C2 | semidirect |
| 2. C5×C7×C11×D21 | C2 | semidirect |
| 3. C72×D165 | C2 | semidirect |
| 5. C3×C5×C72×C11 | C22 | semidirect |
| 7. C7×D385 | D3 | semidirect |
| 10. D21⋊D55 | C7 | direct (N × H) |
| 12. C7×C11×D21 | D5 | semidirect |
| 16. C5×C72×C11 | C2×D3 | semidirect |
| 18. C7×D165 | D7 | semidirect |
| 19. C7×D165 | C2×C7 | semidirect |
| 20. C5×C11×D21 | C2×C7 | semidirect |
| 22. C3×D385 | C2×C7 | semidirect |
| 25. C3×C72×C11 | C2×D5 | semidirect |
| 29. C5×C7×D21 | D11 | semidirect |
| 32. C3×C5×C7×C11 | C2×D7 | semidirect |
| 33. C3×C5×C7×C11 | C22×C7 | semidirect |
| 41. D385 | D3×C7 | semidirect |
| 47. C3×C5×C72 | C2×D11 | semidirect |
| 50. C72×C11 | D3×D5 | semidirect |
| 54. C11×D21 | C7×D5 | semidirect |
| 64. C5×C7×C11 | D3×D7 | semidirect |
| 65. C5×C7×C11 | C2×D3×C7 | semidirect |
| 66. D165 | C7×D7 | semidirect |
| 71. C7×D21 | D55 | semidirect |
| 74. C5×C72 | D3×D11 | semidirect |
| 76. C3×C7×C11 | D5×D7 | semidirect |
| 77. C3×C7×C11 | C2×C7×D5 | semidirect |
| 82. C5×D21 | C7×D11 | semidirect |
| 87. C3×C5×C11 | C2×C7×D7 | semidirect |
| 95. C3×C72 | C2×D55 | semidirect |
| 103. C3×C5×C7 | D7×D11 | semidirect |
| 104. C3×C5×C7 | C2×C7×D11 | semidirect |
| 111. C7×C11 | D3×C7×D5 | semidirect |
| 112. C7×C11 | D15⋊D7 | semidirect |
| 124. C5×C11 | D3×C7×D7 | semidirect |
| 125. C72 | D3×D55 | semidirect |
| 128. D21 | C7×D55 | semidirect |
| 135. C5×C7 | D3×C7×D11 | semidirect |
| 136. C5×C7 | D21⋊D11 | semidirect |
| 137. C3×C11 | C7×D5×D7 | semidirect |
| 147. C3×C7 | D7×D55 | semidirect |
| 148. C3×C7 | C2×C7×D55 | semidirect |
| 150. C3×C5 | C7×D7×D11 | semidirect |
| 159. C11 | C7×D15⋊D7 | semidirect |
| 164. C7 | D3×C7×D55 | semidirect |
| 165. C7 | D21⋊D55 | direct (N × H) |
| 169. C5 | C7×D21⋊D11 | semidirect |
| 171. C3 | C7×D7×D55 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×D385 | 2 |
| C5×C7×C11×D21 | 2 |
| C72×D165 | 2 |
| C7×D7×D55 | 3 |
| C7×D21⋊D11 | 5 |
| D21⋊D55 | 7 |
| D3×C7×D55 | 7 |
| C7×D15⋊D7 | 11 |