Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
172 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 80. C32×C5 | #101 | semidirect |
| 127. C3×C5 | #824 | semidirect |
| 128. C3×C5 | #836 | semidirect |
| 144. C32 | #4005 | semidirect |
| 158. C5 | #63560 | semidirect |
| 165. C3 | #91175 | semidirect |
| 166. C3 | #91234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1204 | 2 |
| #10624097 | 2 |
| C3×#6762 | 2 |
| #91234 | 3 |
| #91175 | 3 |
| #63560 | 5 |