Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 108 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 | direct (N × H) |
| 35. C32×C4×C5 | Q8 | semidirect |
| 95. C3×C4×C5 | Dic6 | semidirect |
| 96. C3×C4×C5 | Dic6 | semidirect |
| 124. C32×C5 | C4×Q8 | semidirect |
| 134. C32×C4 | Dic10 | semidirect |
| 173. C4×C5 | #627 | semidirect |
| 189. C3×C5 | C4×Dic6 | semidirect |
| 190. C3×C5 | C4×Dic6 | semidirect |
| 199. C3×C4 | #1204 | semidirect |
| 200. C3×C4 | Dic30 | semidirect |
| 214. C32 | C4×Dic10 | semidirect |
| 232. C5 | C4×#627 | semidirect |
| 240. C4 | #67153 | direct (N × H) |
| 242. C3 | C4×#1204 | 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 |
| C4×C3⋊Dic15 | 2 |
| C3×C4×Dic15 | 2 |
| C3×C4×C5×Dic3 | 2 |
| Dic3⋊Dic15 | 2 |
| #10623815 | 2 |
| #10623814 | 2 |
| C4×Dic30 | 3 |
| C4×#1204 | 3 |
| C4×#627 | 5 |