Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
196 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 48 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. #10624093 | C2 | semidirect |
| 3. C3×C4×ΓL(1,𝔽16) | C2 | semidirect |
| 7. C3×D60 | C4 | semidirect |
| 8. C3×C5×Dic6 | C4 | semidirect |
| 16. C4×ΓL(1,𝔽16) | D3 | semidirect |
| 34. D60 | Dic3 | semidirect |
| 35. C5×Dic6 | Dic3 | semidirect |
| 60. C3×Dic6 | AGL(1,𝔽5) | semidirect |
| 84. C32×C5 | #104 | semidirect |
| 119. Dic6 | ΓL(1,𝔽16) | semidirect |
| 136. C3×C5 | #805 | semidirect |
| 137. C3×C5 | #837 | semidirect |
| 156. C32 | #4010 | semidirect |
| 172. C5 | #63569 | semidirect |
| 180. C3 | #91158 | semidirect |
| 181. C3 | #91239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6773 | 2 |
| #10624093 | 2 |
| C3×C4×ΓL(1,𝔽16) | 2 |
| #91239 | 3 |
| #91158 | 3 |
| #63569 | 5 |