Finite Group DatabasebetaFinite Group Databasebeta← C32×Dic3×AGL(1,𝔽5) #72254751
Order 2160.
488 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 5. C3×Dic3×AGL(1,𝔽5) | C3 | direct (N × H) |
| 7. C32×ΓL(1,𝔽16) | C4 | semidirect |
| 8. C33×AGL(1,𝔽5) | C4 | semidirect |
| 9. C32×Dic15 | C4 | semidirect |
| 10. C32×C5×Dic3 | C4 | semidirect |
| 23. Dic3×AGL(1,𝔽5) | C32 | direct (N × H) |
| 30. C3×ΓL(1,𝔽16) | C3×C4 | semidirect |
| 33. C32×AGL(1,𝔽5) | Dic3 | direct (N × H) |
| 34. C32×AGL(1,𝔽5) | C3×C4 | semidirect |
| 36. C3×Dic15 | C3×C4 | semidirect |
| 37. C3×C5×Dic3 | C3×C4 | semidirect |
| 41. C33×C5 | C42 | semidirect |
| 53. C32×Dic3 | AGL(1,𝔽5) | direct (N × H) |
| 74. ΓL(1,𝔽16) | C32×C4 | semidirect |
| 77. C3×AGL(1,𝔽5) | C3×Dic3 | direct (N × H) |
| 78. C3×AGL(1,𝔽5) | C32×C4 | semidirect |
| 80. Dic15 | C32×C4 | semidirect |
| 82. C5×Dic3 | C32×C4 | semidirect |
| 89. C32×C5 | C4×Dic3 | semidirect |
| 90. C32×C5 | C3×C42 | semidirect |
| 105. C3×Dic3 | C3×AGL(1,𝔽5) | direct (N × H) |
| 115. C33 | C4×AGL(1,𝔽5) | semidirect |
| 125. AGL(1,𝔽5) | C32×Dic3 | direct (N × H) |
| 139. C3×C5 | C3×C4×Dic3 | semidirect |
| 140. C3×C5 | C32×C42 | semidirect |
| 152. Dic3 | C32×AGL(1,𝔽5) | direct (N × H) |
| 157. C32 | Dic3×AGL(1,𝔽5) | direct (N × H) |
| 158. C32 | C3×C4×AGL(1,𝔽5) | semidirect |
| 171. C5 | C32×C4×Dic3 | semidirect |
| 178. C3 | C3×Dic3×AGL(1,𝔽5) | direct (N × H) |
| 179. C3 | C32×C4×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×ΓL(1,𝔽16) | 2 |
| C2×C33×AGL(1,𝔽5) | 2 |
| C32×D5×Dic3 | 2 |
| C32×C4×AGL(1,𝔽5) | 3 |
| C3×Dic3×AGL(1,𝔽5) | 3 |
| C32×C4×Dic3 | 5 |