Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C3×#6817 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 4. #10623824 | C2 | semidirect |
| 5. #10623821 | C2 | semidirect |
| 13. C3×D60 | C22 | semidirect |
| 15. C3×Dic30 | C22 | semidirect |
| 16. C3×C3⋊#168 | C22 | semidirect |
| 18. #6817 | D3 | semidirect |
| 23. #6710 | D3 | semidirect |
| 37. C2×C4⋊(C3⋊D3) | D5 | semidirect |
| 49. D60 | C2×D3 | semidirect |
| 51. Dic30 | C2×D3 | semidirect |
| 62. C3⋊#168 | C2×D3 | semidirect |
| 114. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 182. C3×C5 | #908 | semidirect |
| 183. C3×C5 | #949 | semidirect |
| 207. C32 | #4078 | semidirect |
| 228. C5 | #63825 | semidirect |
| 237. C3 | #91299 | semidirect |
| 238. C3 | #91304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C3×#6817 | 2 |
| C3×#6710 | 2 |
| #10623824 | 2 |
| #10623821 | 2 |
| #91304 | 3 |
| #91299 | 3 |
| #63825 | 5 |