Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
250 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 9. #91379 | C3 | direct (N × H) |
| 120. C32×C5 | #125 | semidirect |
| 182. C3×C5 | #889 | semidirect |
| 183. C3×C5 | C3×#125 | semidirect |
| 207. C32 | #4016 | semidirect |
| 224. C5 | C3×#889 | semidirect |
| 234. C3 | #91379 | direct (N × H) |
| 235. C3 | C3×#4016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6712 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C32×#683 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×#6669 | 2 |
| C3×#6668 | 2 |
| C3×#4016 | 3 |
| #91379 | 3 |
| C3×#889 | 5 |