Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 4. C3×#6712 | C2 | semidirect |
| 5. #10623831 | C2 | semidirect |
| 7. #10623828 | C2 | semidirect |
| 17. #67154 | C4 | semidirect |
| 22. #6712 | D3 | semidirect |
| 46. C4×C3⋊Dic3 | D5 | semidirect |
| 131. C32×C5 | #117 | semidirect |
| 203. C3×C5 | #877 | semidirect |
| 204. C3×C5 | #892 | semidirect |
| 233. C32 | #4018 | semidirect |
| 253. C5 | #63878 | semidirect |
| 265. C3 | #91393 | semidirect |
| 266. C3 | #91403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67154 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×#6714 | 2 |
| C3×#6712 | 2 |
| #10623831 | 2 |
| #10623829 | 2 |
| #10623828 | 2 |
| #91403 | 3 |
| #91393 | 3 |
| #63878 | 5 |