Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C2×#67180 | C2 | semidirect |
| 3. C3×C4⋊Dic15 | C2 | semidirect |
| 4. #10623814 | C2 | semidirect |
| 22. C4⋊Dic15 | D3 | semidirect |
| 30. C2×C3×C5×D3 | Q8 | semidirect |
| 84. C2×C5×D3 | Dic6 | semidirect |
| 106. C32×C5 | C22⋊Q8 | semidirect |
| 117. C2×C3×D3 | Dic10 | semidirect |
| 169. C3×C5 | #897 | semidirect |
| 170. C3×C5 | #924 | semidirect |
| 179. C2×D3 | Dic30 | semidirect |
| 194. C32 | #4070 | semidirect |
| 213. C5 | #63857 | semidirect |
| 223. C3 | #91365 | semidirect |
| 224. C3 | #91813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C2×C3×C4×C5×D3 | 2 |
| C3×C4⋊Dic15 | 2 |
| #10623814 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #91813 | 3 |
| #91365 | 3 |
| #63857 | 5 |