Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 76 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×Q8×D15 | C2 | semidirect |
| 3. C3×C5×#216 | C2 | semidirect |
| 4. C32×#688 | C2 | semidirect |
| 5. C3×#6663 | C2 | semidirect |
| 6. C3×#6657 | C2 | semidirect |
| 7. C3×#6651 | C2 | semidirect |
| 9. #91522 | C3 | direct (N × H) |
| 22. Q8×D15 | C2×C3 | semidirect |
| 27. C5×#216 | C2×C3 | semidirect |
| 30. C3×#688 | D3 | semidirect |
| 31. C3×#688 | C2×C3 | semidirect |
| 34. #6663 | C2×C3 | semidirect |
| 35. #6657 | C2×C3 | semidirect |
| 36. #6651 | C2×C3 | semidirect |
| 48. C3×#216 | D5 | semidirect |
| 86. #688 | C3×D3 | semidirect |
| 128. #216 | C3×D5 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 203. C3×C5 | #915 | semidirect |
| 204. C3×C5 | C3×#137 | semidirect |
| 225. C32 | #4064 | semidirect |
| 245. C5 | C3×#915 | semidirect |
| 254. C3 | #91522 | direct (N × H) |
| 255. C3 | C3×#4064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D15 | 2 |
| C3×#6766 | 2 |
| C3×C5×#216 | 2 |
| C32×#688 | 2 |
| C3×#6663 | 2 |
| C3×#6657 | 2 |
| C3×#6651 | 2 |
| C3×#4064 | 3 |
| #91522 | 3 |
| C3×#915 | 5 |