Finite Group DatabasebetaFinite Group DatabasebetaOrder 23940.
176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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×C7×C19 | C22×C3 |
| LCS | G ▷ C3×C5×C7×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19⋊C3×D105 | C2 | semidirect |
| 2. C7×D15×C19⋊C3 | C2 | semidirect |
| 3. C3×C5×D7×C19⋊C3 | C2 | semidirect |
| 4. D7×C19×D15 | C3 | semidirect |
| 6. C3×C5×C7×C19⋊C3 | C22 | semidirect |
| 11. C5×D7×C19⋊C3 | D3 | semidirect |
| 12. C19×D105 | C2×C3 | semidirect |
| 13. C7×C19×D15 | C2×C3 | semidirect |
| 14. C3×C5×D7×C19 | C2×C3 | semidirect |
| 19. C3×D7×C19⋊C3 | D5 | semidirect |
| 20. C3×C5×C7×C19 | C22×C3 | semidirect |
| 22. C5×C7×C19⋊C3 | C2×D3 | semidirect |
| 25. D15×C19⋊C3 | D7 | direct (N × H) |
| 30. C5×D7×C19 | C3×D3 | semidirect |
| 32. C3×C7×C19⋊C3 | C2×D5 | semidirect |
| 35. C3×C5×C19⋊C3 | C2×D7 | semidirect |
| 38. C3×D7×C19 | C3×D5 | semidirect |
| 42. D7×C19⋊C3 | D15 | direct (N × H) |
| 44. C5×C7×C19 | C2×C3×D3 | semidirect |
| 50. C19×D15 | C3×D7 | semidirect |
| 56. D7×D15 | C19⋊C3 | direct (N × H) |
| 58. C3×C7×C19 | C2×C3×D5 | semidirect |
| 60. C7×C19⋊C3 | C2×D15 | semidirect |
| 66. C3×C5×C19 | C2×C3×D7 | semidirect |
| 68. C5×C19⋊C3 | D3×D7 | semidirect |
| 71. D7×C19 | C3×D15 | semidirect |
| 75. D105 | C2×C19⋊C3 | semidirect |
| 76. C7×D15 | C2×C19⋊C3 | semidirect |
| 81. C3×C5×D7 | C2×C19⋊C3 | semidirect |
| 86. C3×C19⋊C3 | D5×D7 | semidirect |
| 88. C7×C19 | C2×C3×D15 | semidirect |
| 101. C3×C5×C7 | C22×C19⋊C3 | semidirect |
| 102. C5×C19 | C3×D3×D7 | semidirect |
| 110. C5×D7 | D3×C19⋊C3 | semidirect |
| 115. C3×C19 | C3×D5×D7 | semidirect |
| 117. C19⋊C3 | D7×D15 | direct (N × H) |
| 124. C3×D7 | D5×C19⋊C3 | semidirect |
| 130. C5×C7 | C2×D3×C19⋊C3 | semidirect |
| 135. D15 | D7×C19⋊C3 | direct (N × H) |
| 141. C3×C7 | C2×D5×C19⋊C3 | semidirect |
| 143. C19 | C3×D7×D15 | semidirect |
| 149. C3×C5 | C2×D7×C19⋊C3 | semidirect |
| 152. D7 | D15×C19⋊C3 | direct (N × H) |
| 159. C7 | C2×D15×C19⋊C3 | semidirect |
| 167. C5 | D3×D7×C19⋊C3 | semidirect |
| 171. C3 | D5×D7×C19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19⋊C3×D105 | 2 |
| C7×D15×C19⋊C3 | 2 |
| C3×C5×D7×C19⋊C3 | 2 |
| D7×C19×D15 | 3 |
| D5×D7×C19⋊C3 | 3 |
| D3×D7×C19⋊C3 | 5 |
| C2×D15×C19⋊C3 | 7 |
| C3×D7×D15 | 19 |