Finite Group DatabasebetaFinite Group DatabasebetaOrder 32340.
208 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 208 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 | C5 | D21×D77 |
| commutator, cosocle, hypocenter | C3×C72×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C11 | C22 |
| LCS | G ▷ C3×C72×C11 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×C7×D77 | C2 | semidirect |
| 2. C5×C7×C11×D21 | C2 | semidirect |
| 3. C5×C3⋊(C7⋊D77) | C2 | semidirect |
| 5. C3×C5×C72×C11 | C22 | semidirect |
| 6. D21×D77 | C5 | direct (N × H) |
| 8. C5×C7×D77 | D3 | semidirect |
| 12. C3⋊(C7⋊D77) | C2×C5 | semidirect |
| 13. C7×C11×D21 | C2×C5 | semidirect |
| 14. C3×C7×D77 | C2×C5 | semidirect |
| 16. C5×C72×C11 | C2×D3 | semidirect |
| 20. C5×C11×D21 | D7 | semidirect |
| 22. C3×C5×D77 | D7 | semidirect |
| 25. C3×C72×C11 | C22×C5 | semidirect |
| 29. C5×C7×D21 | D11 | semidirect |
| 32. C3×C5×C7×C11 | C2×D7 | semidirect |
| 33. C3×C5×C7×C11 | C2×D7 | semidirect |
| 35. C7×D77 | C5×D3 | semidirect |
| 44. C5×D77 | D21 | direct (N × H) |
| 47. C3×C5×C72 | C2×D11 | semidirect |
| 50. C72×C11 | C2×C5×D3 | semidirect |
| 57. C11×D21 | C5×D7 | semidirect |
| 59. C3×D77 | C5×D7 | semidirect |
| 64. C5×C7×C11 | D3×D7 | semidirect |
| 65. C5×C7×C11 | C2×D21 | semidirect |
| 72. C7×D21 | C5×D11 | semidirect |
| 74. C5×C72 | D3×D11 | semidirect |
| 76. C3×C7×C11 | C2×C5×D7 | semidirect |
| 77. C3×C7×C11 | C2×C5×D7 | semidirect |
| 83. C5×D21 | D77 | direct (N × H) |
| 87. C3×C5×C11 | D72 | semidirect |
| 92. D77 | C5×D21 | direct (N × H) |
| 95. C3×C72 | C2×C5×D11 | semidirect |
| 103. C3×C5×C7 | D7×D11 | semidirect |
| 104. C3×C5×C7 | C2×D77 | semidirect |
| 111. C7×C11 | C5×D3×D7 | semidirect |
| 112. C7×C11 | C2×C5×D21 | semidirect |
| 124. C5×C11 | D7×D21 | semidirect |
| 125. C72 | C5×D3×D11 | semidirect |
| 131. D21 | C5×D77 | direct (N × H) |
| 135. C5×C7 | D11×D21 | semidirect |
| 136. C5×C7 | D3×D77 | semidirect |
| 137. C3×C11 | C5×D72 | semidirect |
| 147. C3×C7 | C5×D7×D11 | semidirect |
| 148. C3×C7 | C2×C5×D77 | semidirect |
| 150. C3×C5 | D7×D77 | semidirect |
| 159. C11 | C5×D7×D21 | semidirect |
| 164. C7 | C5×D11×D21 | semidirect |
| 165. C7 | C5×D3×D77 | semidirect |
| 169. C5 | D21×D77 | direct (N × H) |
| 171. C3 | C5×D7×D77 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C7×D77 | 2 |
| C5×C7×C11×D21 | 2 |
| C5×C3⋊(C7⋊D77) | 2 |
| C5×D7×D77 | 3 |
| D21×D77 | 5 |
| C5×D3×D77 | 7 |
| C5×D11×D21 | 7 |
| C5×D7×D21 | 11 |