Finite Group DatabasebetaFinite Group DatabasebetaOrder 14700.
252 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 252 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×D35 |
| commutator, cosocle, hypocenter | C3×C5×C72 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C22 |
| LCS | G ▷ C3×C5×C72 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C3⋊(C5⋊(C7⋊D7)) | C2 | semidirect |
| 2. C52×C7×D21 | C2 | semidirect |
| 3. C3×C5×C7×D35 | C2 | semidirect |
| 5. C3×C52×C72 | C22 | semidirect |
| 6. D21×D35 | C5 | direct (N × H) |
| 9. C5×C7×D35 | D3 | semidirect |
| 13. C3⋊(C5⋊(C7⋊D7)) | C2×C5 | semidirect |
| 16. C5×C7×D21 | D5 | semidirect |
| 17. C5×C7×D21 | C2×C5 | semidirect |
| 18. C3×C7×D35 | C2×C5 | semidirect |
| 20. C52×C72 | C2×D3 | semidirect |
| 24. C52×D21 | D7 | semidirect |
| 26. C3×C5×D35 | D7 | semidirect |
| 31. C3×C5×C72 | C2×D5 | semidirect |
| 32. C3×C5×C72 | C22×C5 | semidirect |
| 37. C3×C52×C7 | C2×D7 | semidirect |
| 38. C3×C52×C7 | C2×D7 | semidirect |
| 40. C7×D35 | C5×D3 | semidirect |
| 54. C5×D35 | D21 | direct (N × H) |
| 59. C7×D21 | C5×D5 | semidirect |
| 62. C5×C72 | D3×D5 | semidirect |
| 63. C5×C72 | C2×C5×D3 | semidirect |
| 72. C5×D21 | C5×D7 | semidirect |
| 73. C5×D21 | D35 | direct (N × H) |
| 77. C3×D35 | C5×D7 | semidirect |
| 82. C52×C7 | D3×D7 | semidirect |
| 83. C52×C7 | C2×D21 | semidirect |
| 87. C3×C72 | C2×C5×D5 | semidirect |
| 97. C3×C5×C7 | D5×D7 | semidirect |
| 98. C3×C5×C7 | C2×C5×D7 | semidirect |
| 99. C3×C5×C7 | C2×C5×D7 | semidirect |
| 100. C3×C5×C7 | C2×D35 | semidirect |
| 107. C3×C52 | D72 | semidirect |
| 115. D35 | C5×D21 | direct (N × H) |
| 129. C72 | C5×D3×D5 | semidirect |
| 134. D21 | C5×D35 | direct (N × H) |
| 142. C5×C7 | C5×D3×D7 | semidirect |
| 143. C5×C7 | D5×D21 | semidirect |
| 144. C5×C7 | D3×D35 | semidirect |
| 145. C5×C7 | C2×C5×D21 | semidirect |
| 155. C52 | D7×D21 | semidirect |
| 157. C3×C7 | C5×D5×D7 | semidirect |
| 158. C3×C7 | C2×C5×D35 | semidirect |
| 162. C3×C5 | C5×D72 | semidirect |
| 163. C3×C5 | D7×D35 | semidirect |
| 180. C7 | C5×D5×D21 | semidirect |
| 181. C7 | C5×D3×D35 | semidirect |
| 186. C5 | C5×D7×D21 | semidirect |
| 187. C5 | D21×D35 | direct (N × H) |
| 189. C3 | C5×D7×D35 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C3⋊(C5⋊(C7⋊D7)) | 2 |
| C52×C7×D21 | 2 |
| C3×C5×C7×D35 | 2 |
| C5×D7×D35 | 3 |
| D21×D35 | 5 |
| C5×D7×D21 | 5 |
| C5×D3×D35 | 7 |
| C5×D5×D21 | 7 |