Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#67180 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 4. #10623809 | C2 | semidirect |
| 5. #10623805 | C2 | semidirect |
| 25. #6710 | D3 | semidirect |
| 109. C32×C5 | #137 | semidirect |
| 171. C3×C5 | #909 | semidirect |
| 172. C3×C5 | #951 | semidirect |
| 192. C32 | #4097 | semidirect |
| 210. C5 | #63831 | semidirect |
| 218. C3 | #91322 | semidirect |
| 219. C3 | #91840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C3×C5×#235 | 2 |
| C3×#6710 | 2 |
| #10623809 | 2 |
| #10623805 | 2 |
| #91840 | 3 |
| #91322 | 3 |
| #63831 | 5 |