Finite Group DatabasebetaFinite Group DatabasebetaOrder 37620.
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 | D15×D209 |
| commutator, cosocle, hypocenter | C3×C5×C11×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C11×C19 | C22 |
| LCS | G ▷ C3×C5×C11×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C5×D209 | C2 | semidirect |
| 2. C3×C11×C19×D15 | C2 | semidirect |
| 3. C3×D3135 | C2 | semidirect |
| 4. D15×D209 | C3 | direct (N × H) |
| 6. C32×C5×C11×C19 | C22 | semidirect |
| 8. D3135 | C2×C3 | semidirect |
| 9. C11×C19×D15 | C2×C3 | semidirect |
| 13. C3×C5×D209 | D3 | semidirect |
| 14. C3×C5×D209 | C2×C3 | semidirect |
| 18. C32×D209 | D5 | semidirect |
| 21. C3×C5×C11×C19 | C2×D3 | semidirect |
| 22. C3×C5×C11×C19 | C22×C3 | semidirect |
| 27. C5×D209 | C3×D3 | semidirect |
| 29. C32×C11×C19 | C2×D5 | semidirect |
| 31. C3×C19×D15 | D11 | semidirect |
| 38. C3×D209 | C3×D5 | semidirect |
| 39. C3×D209 | D15 | direct (N × H) |
| 42. C5×C11×C19 | C2×C3×D3 | semidirect |
| 44. C3×C11×D15 | D19 | semidirect |
| 46. C32×C5×C19 | C2×D11 | semidirect |
| 52. C3×C11×C19 | C2×C3×D5 | semidirect |
| 53. C3×C11×C19 | C2×D15 | semidirect |
| 55. C19×D15 | C3×D11 | semidirect |
| 61. C32×C5×C11 | C2×D19 | semidirect |
| 64. D209 | C3×D15 | direct (N × H) |
| 71. C11×D15 | C3×D19 | semidirect |
| 78. C3×C5×C19 | D3×D11 | semidirect |
| 79. C3×C5×C19 | C2×C3×D11 | semidirect |
| 83. C11×C19 | C2×C3×D15 | semidirect |
| 91. C32×C19 | D5×D11 | semidirect |
| 93. C3×C5×C11 | D3×D19 | semidirect |
| 94. C3×C5×C11 | C2×C3×D19 | semidirect |
| 107. C32×C11 | D5×D19 | semidirect |
| 108. C5×C19 | C3×D3×D11 | semidirect |
| 111. C3×D15 | D209 | direct (N × H) |
| 123. C3×C19 | C3×D5×D11 | semidirect |
| 124. C3×C19 | D11×D15 | semidirect |
| 125. C5×C11 | C3×D3×D19 | semidirect |
| 126. C32×C5 | C2×D209 | semidirect |
| 133. C3×C11 | C3×D5×D19 | semidirect |
| 134. C3×C11 | D15×D19 | semidirect |
| 139. D15 | C3×D209 | direct (N × H) |
| 146. C19 | C3×D11×D15 | semidirect |
| 151. C3×C5 | D3×D209 | semidirect |
| 152. C3×C5 | C2×C3×D209 | semidirect |
| 155. C11 | C3×D15×D19 | semidirect |
| 159. C32 | D5×D209 | semidirect |
| 167. C5 | C3×D3×D209 | semidirect |
| 170. C3 | C3×D5×D209 | semidirect |
| 171. C3 | D15×D209 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×D209 | 2 |
| C3×C11×C19×D15 | 2 |
| C3×D3135 | 2 |
| D15×D209 | 3 |
| C3×D5×D209 | 3 |
| C3×D3×D209 | 5 |
| C3×D15×D19 | 11 |
| C3×D11×D15 | 19 |