Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
306 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 17. #67153 | C4 | semidirect |
| 41. C3×C5×Dic3 | Q8 | semidirect |
| 107. C5×Dic3 | Dic6 | semidirect |
| 124. C32×C5 | C4×Q8 | semidirect |
| 139. C3×Dic3 | Dic10 | semidirect |
| 189. C3×C5 | C4×Dic6 | semidirect |
| 190. C3×C5 | #887 | semidirect |
| 209. Dic3 | Dic30 | semidirect |
| 214. C32 | C4×Dic10 | semidirect |
| 232. C5 | #63837 | semidirect |
| 242. C3 | #91324 | semidirect |
| 243. C3 | C4×Dic30 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67153 | 2 |
| #10623906 | 2 |
| C3×#6712 | 2 |
| C3×C4×C5×Dic3 | 2 |
| Dic3⋊Dic15 | 2 |
| Dic3×Dic15 | 2 |
| C4×Dic30 | 3 |
| #91324 | 3 |
| #63837 | 5 |