Finite Group DatabasebetaFinite Group DatabasebetaOrder 36540.
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 | C7 | D45⋊D29 |
| commutator, cosocle, hypocenter | C5×C9×C29 | C22×C7 |
| Frattini | C3 | C7×D15⋊D29 |
| Fitting | C5×C7×C9×C29 | C22 |
| socle | C3×C5×C7×C29 | C2×D3 |
| LCS | G ▷ C5×C9×C29 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×C29×D45 | C2 | semidirect |
| 2. C5×C7×D261 | C2 | semidirect |
| 3. C7×C9×D145 | C2 | semidirect |
| 5. C5×C7×C9×C29 | C22 | semidirect |
| 10. D45⋊D29 | C7 | direct (N × H) |
| 12. C7×D261 | D5 | semidirect |
| 16. C29×D45 | C2×C7 | semidirect |
| 17. C5×D261 | C2×C7 | semidirect |
| 18. C9×D145 | C2×C7 | semidirect |
| 20. C7×D145 | D9 | semidirect |
| 23. C7×C9×C29 | C2×D5 | semidirect |
| 25. C5×C9×C29 | C22×C7 | semidirect |
| 31. C5×C7×C29 | C2×D9 | semidirect |
| 36. C7×D45 | D29 | semidirect |
| 41. D261 | C7×D5 | semidirect |
| 50. C5×C7×C9 | C2×D29 | semidirect |
| 51. D145 | C7×D9 | semidirect |
| 54. C9×C29 | C2×C7×D5 | semidirect |
| 59. C7×C29 | D5×D9 | semidirect |
| 64. C5×C29 | C2×C7×D9 | semidirect |
| 71. D45 | C7×D29 | semidirect |
| 79. C7×C9 | D5×D29 | semidirect |
| 84. C5×C9 | C2×C7×D29 | semidirect |
| 89. C5×C7 | D9×D29 | semidirect |
| 93. C29 | C7×D5×D9 | semidirect |
| 108. C9 | C7×D5×D29 | semidirect |
| 109. C7 | D45⋊D29 | direct (N × H) |
| 113. C5 | C7×D9×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C29×D45 | 2 |
| C5×C7×D261 | 2 |
| C7×C9×D145 | 2 |
| C7×D15⋊D29 | 3 |
| C7×D9×D29 | 5 |
| D45⋊D29 | 7 |
| C7×D5×D9 | 29 |