Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
342 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 1. C2×C32×C5×Q8 | C2 | semidirect |
| 3. C3×#6714 | C2 | semidirect |
| 4. C3×C4×Dic15 | C2 | semidirect |
| 5. #91836 | C3 | direct (N × H) |
| 15. C2×C3×C5×Q8 | D3 | semidirect |
| 16. C2×C3×C5×Q8 | C2×C3 | semidirect |
| 19. #6714 | C2×C3 | semidirect |
| 20. C4×Dic15 | C2×C3 | semidirect |
| 30. C2×C32×Q8 | D5 | semidirect |
| 54. C2×C5×Q8 | C3×D3 | semidirect |
| 80. C2×C3×Q8 | C3×D5 | semidirect |
| 81. C2×C3×Q8 | D15 | semidirect |
| 88. C32×C5 | #124 | semidirect |
| 134. C2×Q8 | C3×D15 | semidirect |
| 139. C3×C5 | #947 | semidirect |
| 140. C3×C5 | C3×#124 | semidirect |
| 159. C32 | #4093 | semidirect |
| 174. C5 | C3×#947 | semidirect |
| 182. C3 | C3×#4093 | semidirect |
| 183. C3 | #91836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C2×C3×D60 | 2 |
| C3×#6714 | 2 |
| C3×C4×Dic15 | 2 |
| #91836 | 3 |
| C3×#4093 | 3 |
| C3×#947 | 5 |