Finite Group DatabasebetaFinite Group DatabasebetaOrder 14700.
288 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C72 | C22 |
| LCS | G ▷ C3×C52×C72 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊(C5⋊(C5⋊(C7⋊D7))) | C2 | semidirect |
| 2. C5×C7×D105 | C2 | semidirect |
| 3. C3×C5×C7×D35 | C2 | semidirect |
| 5. C3×C52×C72 | C22 | semidirect |
| 10. C5×C7×D35 | D3 | semidirect |
| 16. C7×D105 | D5 | semidirect |
| 18. C3×C7×D35 | D5 | semidirect |
| 20. C52×C72 | C2×D3 | semidirect |
| 24. C5×D105 | D7 | semidirect |
| 26. C3×C5×D35 | D7 | semidirect |
| 31. C3×C5×C72 | C2×D5 | semidirect |
| 32. C3×C5×C72 | C2×D5 | semidirect |
| 37. C3×C52×C7 | C2×D7 | semidirect |
| 38. C3×C52×C7 | C2×D7 | semidirect |
| 43. C7×D35 | D15 | semidirect |
| 54. C5×D35 | D21 | semidirect |
| 62. C5×C72 | D3×D5 | semidirect |
| 63. C5×C72 | C2×D15 | semidirect |
| 74. D105 | D35 | direct (N × H) |
| 78. C3×D35 | D35 | semidirect |
| 83. C52×C7 | D3×D7 | semidirect |
| 84. C52×C7 | C2×D21 | semidirect |
| 88. C3×C72 | D52 | semidirect |
| 98. C3×C5×C7 | D5×D7 | semidirect |
| 99. C3×C5×C7 | D5×D7 | semidirect |
| 100. C3×C5×C7 | C2×D35 | semidirect |
| 101. C3×C5×C7 | C2×D35 | semidirect |
| 108. C3×C52 | D72 | semidirect |
| 121. D35 | D105 | direct (N × H) |
| 131. C72 | D5×D15 | semidirect |
| 144. C5×C7 | D7×D15 | semidirect |
| 145. C5×C7 | D5×D21 | semidirect |
| 146. C5×C7 | D3×D35 | semidirect |
| 147. C5×C7 | C2×D105 | semidirect |
| 157. C52 | D7×D21 | semidirect |
| 159. C3×C7 | D5×D35 | semidirect |
| 160. C3×C7 | D5×D35 | semidirect |
| 164. C3×C5 | D7×D35 | semidirect |
| 165. C3×C5 | D7×D35 | semidirect |
| 182. C7 | D5×D105 | semidirect |
| 183. C7 | D15×D35 | semidirect |
| 188. C5 | D7×D105 | semidirect |
| 189. C5 | D21×D35 | semidirect |
| 191. C3 | D352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C5⋊(C5⋊(C7⋊D7))) | 2 |
| C5×C7×D105 | 2 |
| C3×C5×C7×D35 | 2 |
| D352 | 3 |
| D21×D35 | 5 |
| D7×D105 | 5 |
| D15×D35 | 7 |
| D5×D105 | 7 |