Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 62 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. C3×D3×Dic10 | C2 | semidirect |
| 3. #10623826 | C2 | semidirect |
| 4. #10623802 | C2 | semidirect |
| 5. #10623796 | C2 | semidirect |
| 6. #10623766 | C2 | semidirect |
| 7. C3×#6656 | C2 | semidirect |
| 25. D3×Dic10 | D3 | semidirect |
| 35. #6656 | D3 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 202. C3×C5 | #915 | semidirect |
| 203. C3×C5 | #942 | semidirect |
| 224. C32 | #4097 | semidirect |
| 243. C5 | #63946 | semidirect |
| 252. C3 | #91309 | semidirect |
| 253. C3 | #91486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3795 | 2 |
| C3×D3×Dic10 | 2 |
| #10623826 | 2 |
| #10623802 | 2 |
| #10623796 | 2 |
| #10623766 | 2 |
| C3×#6656 | 2 |
| #91486 | 3 |
| #91309 | 3 |
| #63946 | 5 |