Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. C3×#6712 | C2 | semidirect |
| 5. #10623831 | C2 | semidirect |
| 14. #67155 | C4 | semidirect |
| 20. #6712 | D3 | semidirect |
| 31. C3×Dic15 | C2×C4 | semidirect |
| 56. C5×C3⋊D3 | C4⋊C4 | semidirect |
| 81. Dic15 | C4×D3 | semidirect |
| 94. C32×C5 | C2×C4⋊C4 | semidirect |
| 145. C3⋊D3 | #683 | semidirect |
| 152. C3×C5 | D3×C4⋊C4 | semidirect |
| 173. C32 | C2×#683 | semidirect |
| 190. C5 | #63883 | semidirect |
| 200. C3 | D3×#683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×#67155 | 2 |
| C3×#6712 | 2 |
| #10623831 | 2 |
| D3×#683 | 3 |
| #63883 | 5 |