Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 270 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. C3×#6817 | C2 | semidirect |
| 2. C3×C5×#235 | C2 | semidirect |
| 3. C2×C3⋊(C3⋊#168) | C2 | semidirect |
| 4. #10623807 | C2 | semidirect |
| 5. #10623802 | C2 | semidirect |
| 6. #10623801 | C2 | semidirect |
| 7. #10623798 | C2 | semidirect |
| 23. #6817 | D3 | semidirect |
| 24. C5×#235 | D3 | semidirect |
| 46. C3×#235 | D5 | semidirect |
| 121. #235 | D15 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 207. C3×C5 | #950 | semidirect |
| 208. C3×C5 | #950 | semidirect |
| 230. C32 | #4096 | semidirect |
| 252. C5 | #63822 | semidirect |
| 261. C3 | #91297 | semidirect |
| 262. C3 | #91839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C3×C5×#235 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| #10623807 | 2 |
| #10623802 | 2 |
| #10623801 | 2 |
| #10623798 | 2 |
| #91839 | 3 |
| #91297 | 3 |
| #63822 | 5 |