Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
346 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 92 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×#1200 | C2 | semidirect |
| 3. C3×C5×#217 | C2 | semidirect |
| 4. C32×C22⋊Dic5 | C2 | semidirect |
| 5. C3×Dic3⋊Dic5 | C2 | semidirect |
| 6. C3×#6668 | C2 | semidirect |
| 7. C3×#6667 | C2 | semidirect |
| 9. #91562 | C3 | direct (N × H) |
| 23. C2×#1200 | C2×C3 | semidirect |
| 25. C5×#217 | C2×C3 | semidirect |
| 27. C3×C22⋊Dic5 | D3 | semidirect |
| 28. C3×C22⋊Dic5 | C2×C3 | semidirect |
| 32. Dic3⋊Dic5 | C2×C3 | semidirect |
| 33. #6668 | C2×C3 | semidirect |
| 34. #6667 | C2×C3 | semidirect |
| 51. C3×#217 | D5 | semidirect |
| 86. C22⋊Dic5 | C3×D3 | semidirect |
| 140. #217 | C3×D5 | semidirect |
| 144. C32×C5 | #123 | semidirect |
| 227. C3×C5 | #883 | semidirect |
| 228. C3×C5 | C3×#123 | semidirect |
| 264. C32 | #4029 | semidirect |
| 288. C5 | C3×#883 | semidirect |
| 302. C3 | #91562 | direct (N × H) |
| 303. C3 | C3×#4029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1220 | 2 |
| C2×C3×#1200 | 2 |
| C3×C5×#217 | 2 |
| C32×C22⋊Dic5 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×#6668 | 2 |
| C3×#6667 | 2 |
| C3×#4029 | 3 |
| #91562 | 3 |
| C3×#883 | 5 |