Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10624283 | C2 | semidirect |
| 2. C2×C3×C5×D12 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 4. #10623805 | C2 | semidirect |
| 5. #10623800 | C2 | semidirect |
| 11. C4⋊(C3⋊D15) | C22 | semidirect |
| 13. #67180 | C22 | semidirect |
| 16. C3×C3⋊#168 | C22 | semidirect |
| 22. C2×C5×D12 | D3 | semidirect |
| 25. #6710 | D3 | semidirect |
| 38. C2×C3×D12 | D5 | semidirect |
| 63. C3⋊#168 | C2×D3 | semidirect |
| 108. C2×D12 | D15 | semidirect |
| 115. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 184. C3×C5 | #908 | semidirect |
| 185. C3×C5 | #932 | semidirect |
| 209. C32 | #4078 | semidirect |
| 230. C5 | #63830 | semidirect |
| 239. C3 | #91304 | semidirect |
| 240. C3 | #91821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624283 | 2 |
| C2×C3×C5×D12 | 2 |
| C3×#6710 | 2 |
| #10623805 | 2 |
| #10623800 | 2 |
| #91821 | 3 |
| #91304 | 3 |
| #63830 | 5 |