Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 108 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. C3×C5×#208 | C2 | semidirect |
| 3. C32×#681 | C2 | semidirect |
| 4. C3×#6651 | C2 | semidirect |
| 5. C3×#6648 | C2 | semidirect |
| 7. #91292 | C3 | direct (N × H) |
| 15. C3×C5×C3⋊C8 | C22 | semidirect |
| 16. C32×#168 | C22 | semidirect |
| 21. C5×#208 | C2×C3 | semidirect |
| 23. C3×#681 | D3 | semidirect |
| 24. C3×#681 | C2×C3 | semidirect |
| 27. #6651 | C2×C3 | semidirect |
| 28. #6648 | C2×C3 | semidirect |
| 40. C3×#208 | D5 | semidirect |
| 60. C3×#168 | C2×D3 | semidirect |
| 61. C3×#168 | C22×C3 | semidirect |
| 62. C5×C3⋊C8 | C22×C3 | semidirect |
| 68. C3×D15 | M16 | semidirect |
| 71. #681 | C3×D3 | semidirect |
| 82. C3×C3⋊C8 | C2×D5 | semidirect |
| 110. #208 | C3×D5 | semidirect |
| 113. C32×C5 | C2×M16 | semidirect |
| 122. #168 | C2×C3×D3 | semidirect |
| 139. D15 | C3×M16 | semidirect |
| 161. C3⋊C8 | C2×C3×D5 | semidirect |
| 180. C3×C5 | D3×M16 | semidirect |
| 181. C3×C5 | C2×C3×M16 | semidirect |
| 205. C32 | D5×M16 | semidirect |
| 225. C5 | C3×D3×M16 | semidirect |
| 235. C3 | #91292 | direct (N × H) |
| 236. C3 | C3×D5×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D15 | 2 |
| C3×C5×#208 | 2 |
| C32×#681 | 2 |
| C3×#6651 | 2 |
| C3×#6648 | 2 |
| C3×D5×M16 | 3 |
| #91292 | 3 |
| C3×D3×M16 | 5 |