Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
266 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 88 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×C4×Dic15 | C2 | semidirect |
| 3. C32×#683 | C2 | semidirect |
| 4. C3×Dic3⋊Dic5 | C2 | semidirect |
| 5. C3×#6668 | C2 | semidirect |
| 9. #91367 | C3 | direct (N × H) |
| 19. C4×Dic15 | C2×C3 | semidirect |
| 26. C3×#683 | D3 | semidirect |
| 27. C3×#683 | C2×C3 | semidirect |
| 29. Dic3⋊Dic5 | C2×C3 | semidirect |
| 30. #6668 | C2×C3 | semidirect |
| 79. #683 | C3×D3 | semidirect |
| 127. C32×C5 | #126 | semidirect |
| 196. C3×C5 | #898 | semidirect |
| 197. C3×C5 | C3×#126 | semidirect |
| 226. C32 | #4025 | semidirect |
| 245. C5 | C3×#898 | semidirect |
| 257. C3 | #91367 | direct (N × H) |
| 258. C3 | C3×#4025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic15 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C32×#683 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×#6668 | 2 |
| C3×(C2×D3)⋊Dic5 | 2 |
| C3×#4025 | 3 |
| #91367 | 3 |
| C3×#898 | 5 |