Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
206 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. C4×C3⋊#170 | C3 | direct (N × H) |
| 8. C3×C3⋊#170 | C4 | direct (N × H) |
| 16. C32×C4×C5 | C8 | semidirect |
| 17. C32×Dic5 | C8 | semidirect |
| 31. C3⋊#170 | C3×C4 | direct (N × H) |
| 48. C3×C4×C5 | C3⋊C8 | semidirect |
| 49. C3×C4×C5 | C3×C8 | semidirect |
| 52. C3×Dic5 | C3⋊C8 | semidirect |
| 53. C3×Dic5 | C3×C8 | semidirect |
| 61. C32×C5 | C4×C8 | semidirect |
| 69. C32×C4 | #170 | semidirect |
| 92. C4×C5 | C3×C3⋊C8 | semidirect |
| 93. Dic5 | C3×C3⋊C8 | semidirect |
| 101. C3×C5 | C4×C3⋊C8 | semidirect |
| 102. C3×C5 | C3×C4×C8 | semidirect |
| 113. C3×C4 | C3×#170 | semidirect |
| 114. C3×C4 | C3⋊#170 | direct (N × H) |
| 118. C32 | C4×#170 | semidirect |
| 132. C5 | C3×C4×C3⋊C8 | semidirect |
| 136. C4 | C3×C3⋊#170 | direct (N × H) |
| 138. C3 | C3×C4×#170 | semidirect |
| 139. C3 | C4×C3⋊#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#170 | 2 |
| C32×C4×Dic5 | 2 |
| C4×C3⋊#170 | 3 |
| C3×C4×#170 | 3 |
| C3×C4×C3⋊C8 | 5 |