Finite Group DatabasebetaFinite Group DatabasebetaOrder 21420.
176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D21×D85 |
| commutator, cosocle, hypocenter | C3×C5×C7×C17 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C17 | C22 |
| LCS | G ▷ C3×C5×C7×C17 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C7×D85 | C2 | semidirect |
| 2. C3×C5×C17×D21 | C2 | semidirect |
| 3. C3×D1785 | C2 | semidirect |
| 4. D21×D85 | C3 | direct (N × H) |
| 6. C32×C5×C7×C17 | C22 | semidirect |
| 8. D1785 | C2×C3 | semidirect |
| 9. C5×C17×D21 | C2×C3 | semidirect |
| 12. C3×C7×D85 | D3 | semidirect |
| 13. C3×C7×D85 | C2×C3 | semidirect |
| 18. C3×C17×D21 | D5 | semidirect |
| 21. C3×C5×C7×C17 | C2×D3 | semidirect |
| 22. C3×C5×C7×C17 | C22×C3 | semidirect |
| 25. C32×D85 | D7 | semidirect |
| 30. C7×D85 | C3×D3 | semidirect |
| 32. C32×C7×C17 | C2×D5 | semidirect |
| 35. C32×C5×C17 | C2×D7 | semidirect |
| 37. C17×D21 | C3×D5 | semidirect |
| 44. C3×C5×D21 | D17 | semidirect |
| 47. C5×C7×C17 | C2×C3×D3 | semidirect |
| 53. C3×D85 | C3×D7 | semidirect |
| 54. C3×D85 | D21 | direct (N × H) |
| 59. C3×C7×C17 | D3×D5 | semidirect |
| 60. C3×C7×C17 | C2×C3×D5 | semidirect |
| 62. C32×C5×C7 | C2×D17 | semidirect |
| 67. C3×C5×C17 | C2×C3×D7 | semidirect |
| 68. C3×C5×C17 | C2×D21 | semidirect |
| 74. C5×D21 | C3×D17 | semidirect |
| 85. D85 | C3×D21 | direct (N × H) |
| 86. C32×C17 | D5×D7 | semidirect |
| 90. C3×D21 | D85 | direct (N × H) |
| 91. C7×C17 | C3×D3×D5 | semidirect |
| 93. C3×C5×C7 | D3×D17 | semidirect |
| 94. C3×C5×C7 | C2×C3×D17 | semidirect |
| 105. C5×C17 | C2×C3×D21 | semidirect |
| 112. C32×C7 | C2×D85 | semidirect |
| 116. C3×C17 | C3×D5×D7 | semidirect |
| 117. C3×C17 | D5×D21 | semidirect |
| 118. C32×C5 | D7×D17 | semidirect |
| 123. D21 | C3×D85 | direct (N × H) |
| 127. C5×C7 | C3×D3×D17 | semidirect |
| 140. C3×C7 | D3×D85 | semidirect |
| 141. C3×C7 | C2×C3×D85 | semidirect |
| 146. C17 | C3×D5×D21 | semidirect |
| 148. C3×C5 | C3×D7×D17 | semidirect |
| 149. C3×C5 | D17×D21 | semidirect |
| 158. C32 | D7×D85 | semidirect |
| 159. C7 | C3×D3×D85 | semidirect |
| 167. C5 | C3×D17×D21 | semidirect |
| 170. C3 | C3×D7×D85 | semidirect |
| 171. C3 | D21×D85 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C7×D85 | 2 |
| C3×C5×C17×D21 | 2 |
| C3×D1785 | 2 |
| D21×D85 | 3 |
| C3×D7×D85 | 3 |
| C3×D17×D21 | 5 |
| C3×D3×D85 | 7 |
| C3×D5×D21 | 17 |