Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 2. C2×C3×Dic30 | C2 | semidirect |
| 3. C32×C42×C5 | C2 | semidirect |
| 4. C3×#6714 | C2 | semidirect |
| 5. #91764 | C3 | direct (N × H) |
| 15. C2×Dic30 | C2×C3 | semidirect |
| 19. C3×C42×C5 | D3 | semidirect |
| 20. C3×C42×C5 | C2×C3 | semidirect |
| 21. #6714 | C2×C3 | semidirect |
| 32. C32×C42 | D5 | semidirect |
| 55. C42×C5 | C3×D3 | semidirect |
| 84. C3×C42 | C3×D5 | semidirect |
| 85. C3×C42 | D15 | semidirect |
| 87. C32×C5 | #124 | semidirect |
| 135. C42 | C3×D15 | semidirect |
| 137. C3×C5 | #875 | semidirect |
| 138. C3×C5 | C3×#124 | semidirect |
| 157. C32 | #4021 | semidirect |
| 172. C5 | C3×#875 | semidirect |
| 180. C3 | C3×#4021 | semidirect |
| 181. C3 | #91764 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×C3×Dic30 | 2 |
| C32×C42×C5 | 2 |
| C3×#6714 | 2 |
| #91764 | 3 |
| C3×#4021 | 3 |
| C3×#875 | 5 |