Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
366 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 90 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. C22×C3⋊Dic15 | C2 | semidirect |
| 3. C3×#6719 | C2 | semidirect |
| 4. #10623814 | C2 | semidirect |
| 5. (C2×D3)⋊Dic15 | C2 | semidirect |
| 22. #6719 | D3 | semidirect |
| 107. C32×C5 | #123 | semidirect |
| 170. C3×C5 | #886 | semidirect |
| 171. C3×C5 | #935 | semidirect |
| 196. C32 | #4081 | semidirect |
| 215. C5 | #63962 | semidirect |
| 225. C3 | #91543 | semidirect |
| 226. C3 | #91824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊Dic15 | 2 |
| C2×C3×C5×#67 | 2 |
| C3×#6719 | 2 |
| #10623814 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #91824 | 3 |
| #91543 | 3 |
| #63962 | 5 |