Finite Group DatabasebetaFinite Group DatabasebetaOrder 36540.
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 | D35×D87 |
| commutator, cosocle, hypocenter | C3×C5×C7×C29 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C29 | C22 |
| LCS | G ▷ C3×C5×C7×C29 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C29×D35 | C2 | semidirect |
| 2. C3×C5×C7×D87 | C2 | semidirect |
| 3. C3×D3045 | C2 | semidirect |
| 4. D35×D87 | C3 | direct (N × H) |
| 6. C32×C5×C7×C29 | C22 | semidirect |
| 8. D3045 | C2×C3 | semidirect |
| 9. C5×C7×D87 | C2×C3 | semidirect |
| 12. C3×C29×D35 | D3 | semidirect |
| 13. C3×C29×D35 | C2×C3 | semidirect |
| 18. C3×C7×D87 | D5 | semidirect |
| 21. C3×C5×C7×C29 | C2×D3 | semidirect |
| 22. C3×C5×C7×C29 | C22×C3 | semidirect |
| 24. C3×C5×D87 | D7 | semidirect |
| 29. C29×D35 | C3×D3 | semidirect |
| 31. C32×C7×C29 | C2×D5 | semidirect |
| 34. C32×C5×C29 | C2×D7 | semidirect |
| 37. C7×D87 | C3×D5 | semidirect |
| 44. C5×C7×C29 | C2×C3×D3 | semidirect |
| 46. C5×D87 | C3×D7 | semidirect |
| 55. C32×D35 | D29 | semidirect |
| 57. C3×C7×C29 | D3×D5 | semidirect |
| 58. C3×C7×C29 | C2×C3×D5 | semidirect |
| 62. C3×D87 | D35 | direct (N × H) |
| 64. C3×C5×C29 | D3×D7 | semidirect |
| 65. C3×C5×C29 | C2×C3×D7 | semidirect |
| 73. C32×C5×C7 | C2×D29 | semidirect |
| 77. C32×C29 | C2×D35 | semidirect |
| 84. C3×D35 | C3×D29 | semidirect |
| 85. C3×D35 | D87 | direct (N × H) |
| 86. C7×C29 | C3×D3×D5 | semidirect |
| 92. D87 | C3×D35 | direct (N × H) |
| 95. C5×C29 | C3×D3×D7 | semidirect |
| 102. C3×C5×C7 | C2×C3×D29 | semidirect |
| 103. C3×C5×C7 | C2×D87 | semidirect |
| 108. C3×C29 | D3×D35 | semidirect |
| 109. C3×C29 | C2×C3×D35 | semidirect |
| 114. D35 | C3×D87 | direct (N × H) |
| 115. C32×C7 | D5×D29 | semidirect |
| 121. C32×C5 | D7×D29 | semidirect |
| 130. C5×C7 | C2×C3×D87 | semidirect |
| 138. C29 | C3×D3×D35 | semidirect |
| 141. C3×C7 | C3×D5×D29 | semidirect |
| 142. C3×C7 | D5×D87 | semidirect |
| 148. C3×C5 | C3×D7×D29 | semidirect |
| 149. C3×C5 | D7×D87 | semidirect |
| 158. C32 | D29×D35 | semidirect |
| 159. C7 | C3×D5×D87 | semidirect |
| 167. C5 | C3×D7×D87 | semidirect |
| 170. C3 | C3×D29×D35 | semidirect |
| 171. C3 | D35×D87 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C29×D35 | 2 |
| C3×C5×C7×D87 | 2 |
| C3×D3045 | 2 |
| D35×D87 | 3 |
| C3×D29×D35 | 3 |
| C3×D7×D87 | 5 |
| C3×D5×D87 | 7 |
| C3×D3×D35 | 29 |