Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
330 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 79 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×#67158 | C2 | semidirect |
| 4. C3×C4⋊Dic15 | C2 | semidirect |
| 5. C3×#6712 | C2 | semidirect |
| 6. #10623831 | C2 | semidirect |
| 24. C4⋊Dic15 | D3 | semidirect |
| 25. #6712 | D3 | semidirect |
| 38. C2×C5×C3⋊D3 | Q8 | semidirect |
| 137. C32×C5 | C22⋊Q8 | semidirect |
| 150. C2×C3⋊D3 | Dic10 | semidirect |
| 213. C3×C5 | #896 | semidirect |
| 214. C3×C5 | #897 | semidirect |
| 245. C32 | #4024 | semidirect |
| 267. C5 | #63895 | semidirect |
| 279. C3 | #91417 | semidirect |
| 280. C3 | #91436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67158 | 2 |
| C2×#67155 | 2 |
| C5×#3752 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×#6712 | 2 |
| #10623831 | 2 |
| #10623830 | 2 |
| #91436 | 3 |
| #91417 | 3 |
| #63895 | 5 |