Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
298 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 38. C3⋊Dic15 | Q8 | semidirect |
| 40. C3×Dic15 | Q8 | semidirect |
| 108. Dic15 | Dic6 | semidirect |
| 128. C32×C5 | C4⋊Q8 | semidirect |
| 196. C3×C5 | #888 | semidirect |
| 197. C3×C5 | #944 | semidirect |
| 221. C32 | #4090 | semidirect |
| 240. C5 | #63839 | semidirect |
| 250. C3 | #91329 | semidirect |
| 251. C3 | #91833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Dic6 | 2 |
| C2×#67153 | 2 |
| #10623906 | 2 |
| C3×#6712 | 2 |
| #10623815 | 2 |
| #10623814 | 2 |
| Dic3×Dic15 | 2 |
| #91833 | 3 |
| #91329 | 3 |
| #63839 | 5 |