Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 2. C2×C3⋊(C3⋊#168) | C2 | semidirect |
| 3. C3×C5×#208 | C2 | semidirect |
| 4. #10623795 | C2 | semidirect |
| 5. C3⋊C8×D15 | C2 | semidirect |
| 25. C5×#208 | D3 | semidirect |
| 36. C3×#208 | D5 | semidirect |
| 93. #208 | D15 | semidirect |
| 100. C32×C5 | #131 | semidirect |
| 156. C3×C5 | #907 | semidirect |
| 157. C3×C5 | #948 | semidirect |
| 174. C32 | #4053 | semidirect |
| 191. C5 | #63815 | semidirect |
| 198. C3 | #91284 | semidirect |
| 199. C3 | #91796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| C3×C5×#208 | 2 |
| #10623795 | 2 |
| C3⋊C8×D15 | 2 |
| #91796 | 3 |
| #91284 | 3 |
| #63815 | 5 |