Finite Group DatabasebetaFinite Group DatabasebetaOrder 32340.
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C5×C11×C49 | C22 |
| Frattini | C7 | D3×D385 |
| socle | C3×C5×C7×C11 | C2×D7 |
| LCS | G ▷ C3×C5×C11×C49 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D8085 | C2 | semidirect |
| 2. C5×D3×C11×C49 | C2 | semidirect |
| 3. C3×D2695 | C2 | semidirect |
| 5. C3×C5×C11×C49 | C22 | semidirect |
| 8. D2695 | D3 | direct (N × H) |
| 12. D3×C11×C49 | D5 | semidirect |
| 15. C5×C11×C49 | C2×D3 | semidirect |
| 20. C3×C11×C49 | C2×D5 | semidirect |
| 23. C5×D3×C49 | D11 | semidirect |
| 34. C3×C5×C49 | C2×D11 | semidirect |
| 37. C11×C49 | D3×D5 | semidirect |
| 47. C5×D3×C11 | D49 | semidirect |
| 52. D3×C49 | D55 | semidirect |
| 53. C5×C49 | D3×D11 | semidirect |
| 60. C3×C5×C11 | C2×D49 | semidirect |
| 64. C3×C49 | C2×D55 | semidirect |
| 81. D3×C11 | D245 | semidirect |
| 83. C5×C11 | D3×D49 | semidirect |
| 84. C49 | D3×D55 | semidirect |
| 90. C3×C11 | C2×D245 | semidirect |
| 93. C5×D3 | D539 | semidirect |
| 100. C3×C5 | C2×D539 | semidirect |
| 105. C11 | D3×D245 | semidirect |
| 112. D3 | D2695 | direct (N × H) |
| 113. C5 | D3×D539 | semidirect |
| 115. C3 | C2×D2695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8085 | 2 |
| C5×D3×C11×C49 | 2 |
| C3×D2695 | 2 |
| C2×D2695 | 3 |
| D3×D539 | 5 |
| D3×D385 | 7 |
| D3×D245 | 11 |