Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 78 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×#67153 | C2 | semidirect |
| 3. #10623908 | C2 | semidirect |
| 4. C3×C4×Dic15 | C2 | semidirect |
| 5. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #10623813 | C2 | semidirect |
| 7. (C2×D3)⋊Dic15 | C2 | semidirect |
| 30. C4×Dic15 | D3 | semidirect |
| 31. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 51. C3×(C2×D3)⋊C4 | D5 | semidirect |
| 142. (C2×D3)⋊C4 | D15 | semidirect |
| 144. C32×C5 | #124 | semidirect |
| 227. C3×C5 | #875 | semidirect |
| 228. C3×C5 | #885 | semidirect |
| 264. C32 | #4031 | semidirect |
| 288. C5 | #63852 | semidirect |
| 302. C3 | #91350 | semidirect |
| 303. C3 | #91774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67153 | 2 |
| C2×#67152 | 2 |
| #10623908 | 2 |
| C3×C4×Dic15 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| #10623813 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #91774 | 3 |
| #91350 | 3 |
| #63852 | 5 |