Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 6. C2×#4379 | C4 | semidirect |
| 7. C2×C32×C4×C5 | C4 | semidirect |
| 8. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 38. C2×C32×C4 | Dic5 | semidirect |
| 39. C2×C3⋊Dic3 | Dic5 | semidirect |
| 49. C32×C5 | #95 | semidirect |
| 53. C2×C4×C5 | #157 | semidirect |
| 103. C32 | #3963 | semidirect |
| 110. C2×C4 | #4379 | semidirect |
| 116. C5 | #63781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4379 | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| #63781 | 5 |
| #3963 | 9 |