Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×C5×D3×Q8 | C2 | semidirect |
| 3. C3×#6717 | C2 | semidirect |
| 4. C32×#689 | C2 | semidirect |
| 5. C3×#6661 | C2 | semidirect |
| 6. C3×#6660 | C2 | semidirect |
| 7. C3×#6650 | C2 | semidirect |
| 9. #91520 | C3 | direct (N × H) |
| 23. C5×D3×Q8 | C2×C3 | semidirect |
| 26. #6717 | C2×C3 | semidirect |
| 29. C3×#689 | D3 | semidirect |
| 30. C3×#689 | C2×C3 | semidirect |
| 34. #6661 | C2×C3 | semidirect |
| 35. #6660 | C2×C3 | semidirect |
| 36. #6650 | C2×C3 | semidirect |
| 46. C3×D3×Q8 | D5 | semidirect |
| 85. #689 | C3×D3 | semidirect |
| 120. D3×Q8 | C3×D5 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 202. C3×C5 | #918 | semidirect |
| 203. C3×C5 | C3×#137 | semidirect |
| 224. C32 | #4088 | semidirect |
| 243. C5 | C3×#918 | semidirect |
| 252. C3 | #91520 | direct (N × H) |
| 253. C3 | C3×#4088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×Q8 | 2 |
| C3×#6769 | 2 |
| C3×#6717 | 2 |
| C32×#689 | 2 |
| C3×#6661 | 2 |
| C3×#6660 | 2 |
| C3×#6650 | 2 |
| C3×#4088 | 3 |
| #91520 | 3 |
| C3×#918 | 5 |