Finite Group DatabasebetaFinite Group Databasebeta← C7×C5⋊(C5⋊(D7⋊C9)) #36347804
Order 22050.
208 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×C7×C7⋊C9 | C2 | semidirect |
| 7. C5⋊(C5⋊(D7⋊C9)) | C7 | direct (N × H) |
| 8. C7×C5⋊D35 | C9 | semidirect |
| 9. C5×C7×C7⋊C9 | D5 | semidirect |
| 10. C5×C7×C7⋊C9 | D5 | semidirect |
| 12. C52×C7⋊C9 | C2×C7 | semidirect |
| 15. C52×C72 | C2×C9 | semidirect |
| 31. C7×C7⋊C9 | C5⋊D5 | semidirect |
| 32. C5⋊D35 | C7×C9 | semidirect |
| 36. C5×C7⋊C9 | C7×D5 | semidirect |
| 37. C5×C7⋊C9 | C7×D5 | semidirect |
| 39. C5×C72 | C9×D5 | semidirect |
| 40. C5×C72 | C9×D5 | semidirect |
| 47. C52×C7 | D7⋊C9 | semidirect |
| 48. C52×C7 | C2×C7×C9 | semidirect |
| 68. C7⋊C9 | C7×C5⋊D5 | semidirect |
| 70. C72 | C9×C5⋊D5 | semidirect |
| 77. C5×C7 | C5⋊(D7⋊C9) | semidirect |
| 78. C5×C7 | C5⋊(D7⋊C9) | semidirect |
| 79. C5×C7 | C7×C9×D5 | semidirect |
| 80. C5×C7 | C7×C9×D5 | semidirect |
| 83. C52 | C7×D7⋊C9 | semidirect |
| 96. C7 | C5⋊(C5⋊(D7⋊C9)) | direct (N × H) |
| 97. C7 | C7×C9×C5⋊D5 | semidirect |
| 99. C5 | C7×C5⋊(D7⋊C9) | semidirect |
| 100. C5 | C7×C5⋊(D7⋊C9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C7×C7⋊C9 | 2 |
| C3×C7×C5⋊D35 | 3 |
| C7×C5⋊(D7⋊C9) | 5 |
| C7×C9×C5⋊D5 | 7 |
| C5⋊(C5⋊(D7⋊C9)) | 7 |