Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
262 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. C3×#6663 | C2 | direct (N × H) |
| 6. C2×#6663 | C3 | direct (N × H) |
| 24. #6663 | C2×C3 | direct (N × H) |
| 55. C2×C32×C5 | Q16 | semidirect |
| 91. C32×C5 | C2×Q16 | semidirect |
| 108. C2×C3×C5 | Dic12 | semidirect |
| 109. C2×C3×C5 | C3×Q16 | semidirect |
| 135. C2×C32 | #689 | semidirect |
| 142. C3×C5 | C2×Dic12 | semidirect |
| 143. C3×C5 | C2×C3×Q16 | semidirect |
| 157. C2×C5 | C3×Dic12 | semidirect |
| 159. C32 | C2×#689 | semidirect |
| 170. C2×C3 | #6663 | direct (N × H) |
| 171. C2×C3 | C3×#689 | semidirect |
| 174. C5 | C2×C3×Dic12 | semidirect |
| 181. C3 | C2×#6663 | direct (N × H) |
| 182. C3 | C2×C3×#689 | semidirect |
| 183. C2 | C3×#6663 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic30 | 2 |
| C2×C3×C5×Dic6 | 2 |
| C2×C32×#168 | 2 |
| C3×#6663 | 2 |
| C2×C3×#689 | 3 |
| C2×#6663 | 3 |
| C2×C3×Dic12 | 5 |