Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
654 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 142 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. C24×C32×C5 | C2 | semidirect |
| 2. C2×C3×#1220 | C2 | semidirect |
| 3. C3×#6719 | C2 | semidirect |
| 4. #91842 | C3 | direct (N × H) |
| 8. C22×C3×D15 | C22 | semidirect |
| 10. C2×C3×Dic15 | C22 | semidirect |
| 13. C24×C3×C5 | D3 | semidirect |
| 14. C24×C3×C5 | C2×C3 | semidirect |
| 15. C2×#1220 | C2×C3 | semidirect |
| 17. #6719 | C2×C3 | semidirect |
| 21. C22×C32×C5 | D4 | semidirect |
| 26. C24×C32 | D5 | semidirect |
| 35. C22×D15 | C22×C3 | semidirect |
| 38. C2×Dic15 | C22×C3 | semidirect |
| 46. C24×C5 | C3×D3 | semidirect |
| 62. C22×C3×C5 | #67 | semidirect |
| 63. C22×C3×C5 | C3×D4 | semidirect |
| 71. C24×C3 | C3×D5 | semidirect |
| 72. C24×C3 | D15 | semidirect |
| 77. C32×C5 | #120 | semidirect |
| 85. C22×C32 | C22⋊D5 | semidirect |
| 112. C22×C5 | C3×#67 | semidirect |
| 119. C24 | C3×D15 | semidirect |
| 123. C3×C5 | #953 | semidirect |
| 124. C3×C5 | C3×#120 | semidirect |
| 134. C22×C3 | C3×C22⋊D5 | semidirect |
| 135. C22×C3 | #1220 | semidirect |
| 144. C32 | #4099 | semidirect |
| 158. C5 | C3×#953 | semidirect |
| 162. C22 | C3×#1220 | semidirect |
| 166. C3 | C3×#4099 | semidirect |
| 167. C3 | #91842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C5 | 2 |
| C2×C3×#1220 | 2 |
| C3×#6719 | 2 |
| #91842 | 3 |
| C3×#4099 | 3 |
| C3×#953 | 5 |