Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
322 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 86 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×C3×Dic30 | C2 | semidirect |
| 3. #10623906 | C2 | semidirect |
| 5. Dic3⋊Dic15 | C2 | semidirect |
| 6. #10623814 | C2 | semidirect |
| 21. C2×Dic30 | D3 | semidirect |
| 38. C2×C3×C5×D3 | Q8 | semidirect |
| 104. C2×C5×D3 | Dic6 | semidirect |
| 135. C32×C5 | C22⋊Q8 | semidirect |
| 148. C2×C3×D3 | Dic10 | semidirect |
| 210. C3×C5 | #878 | semidirect |
| 211. C3×C5 | #946 | semidirect |
| 220. C2×D3 | Dic30 | semidirect |
| 240. C32 | #4024 | semidirect |
| 261. C5 | #63887 | semidirect |
| 273. C3 | #91410 | semidirect |
| 274. C3 | #91767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic30 | 2 |
| C2×D3×Dic15 | 2 |
| #10623906 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| Dic3⋊Dic15 | 2 |
| #10623814 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #91767 | 3 |
| #91410 | 3 |
| #63887 | 5 |