Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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×C5×C72×C13 | C22 |
| LCS | G ▷ C3×C5×C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5⋊(C7⋊D91) | C2 | semidirect |
| 2. C5×C7×C13×D21 | C2 | semidirect |
| 3. C7×D1365 | C2 | semidirect |
| 5. C3×C5×C72×C13 | C22 | semidirect |
| 7. C5⋊(C7⋊D91) | D3 | semidirect |
| 13. C7×C13×D21 | D5 | semidirect |
| 15. C5×C72×C13 | C2×D3 | semidirect |
| 17. D1365 | D7 | semidirect |
| 19. C5×C13×D21 | D7 | semidirect |
| 25. C3×C72×C13 | C2×D5 | semidirect |
| 29. C5×C7×D21 | D13 | semidirect |
| 32. C3×C5×C7×C13 | C2×D7 | semidirect |
| 33. C3×C5×C7×C13 | C2×D7 | semidirect |
| 48. C3×C5×C72 | C2×D13 | semidirect |
| 49. C72×C13 | D3×D5 | semidirect |
| 52. C13×D21 | D35 | semidirect |
| 62. C5×C7×C13 | D3×D7 | semidirect |
| 63. C5×C7×C13 | D3×D7 | semidirect |
| 72. C7×D21 | D65 | semidirect |
| 75. C3×C7×C13 | D5×D7 | semidirect |
| 76. C3×C7×C13 | C2×D35 | semidirect |
| 78. C5×C72 | D3×D13 | semidirect |
| 81. C5×D21 | D91 | semidirect |
| 87. C3×C5×C13 | D72 | semidirect |
| 96. C3×C72 | C2×D65 | semidirect |
| 103. C3×C5×C7 | D7×D13 | semidirect |
| 104. C3×C5×C7 | C2×D91 | semidirect |
| 109. C7×C13 | D3×D35 | semidirect |
| 110. C7×C13 | D15⋊D7 | semidirect |
| 123. C5×C13 | D21⋊D7 | semidirect |
| 126. C72 | D3×D65 | semidirect |
| 128. D21 | D455 | semidirect |
| 134. C3×C13 | D7×D35 | semidirect |
| 136. C5×C7 | D3×D91 | semidirect |
| 137. C5×C7 | D21⋊D13 | semidirect |
| 147. C3×C7 | D7×D65 | semidirect |
| 148. C3×C7 | C2×D455 | semidirect |
| 150. C3×C5 | D7×D91 | semidirect |
| 158. C13 | D21⋊D35 | semidirect |
| 164. C7 | D3×D455 | semidirect |
| 165. C7 | D21⋊D65 | semidirect |
| 169. C5 | D21⋊D91 | semidirect |
| 171. C3 | D7×D455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5⋊(C7⋊D91) | 2 |
| C5×C7×C13×D21 | 2 |
| C7×D1365 | 2 |
| D7×D455 | 3 |
| D21⋊D91 | 5 |
| D21⋊D65 | 7 |
| D3×D455 | 7 |
| D21⋊D35 | 13 |