Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 2. D3×Dic30 | C2 | semidirect |
| 3. #10623910 | C2 | semidirect |
| 4. C3×#6716 | C2 | semidirect |
| 5. #10623805 | C2 | semidirect |
| 6. #10623802 | C2 | semidirect |
| 7. D3×C3⋊#168 | C2 | semidirect |
| 12. #67180 | C22 | semidirect |
| 13. C3×Dic30 | C22 | semidirect |
| 19. C3⋊(C3⋊#168) | C22 | semidirect |
| 20. C3×C3⋊#168 | C22 | semidirect |
| 31. #6716 | D3 | direct (N × H) |
| 66. Dic30 | C2×D3 | semidirect |
| 76. C3⋊#168 | C2×D3 | semidirect |
| 83. C3×C5×D3 | SD16 | semidirect |
| 136. C32×C5 | C2×SD16 | semidirect |
| 166. C5×D3 | #214 | semidirect |
| 203. C3×D3 | #687 | semidirect |
| 212. C3×C5 | D3×SD16 | semidirect |
| 213. C3×C5 | C2×#214 | semidirect |
| 237. C32 | C2×#687 | semidirect |
| 258. D3 | #6716 | direct (N × H) |
| 259. C5 | D3×#214 | semidirect |
| 269. C3 | D3×#687 | semidirect |
| 270. C3 | C2×#6716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×D4 | 2 |
| D3×Dic30 | 2 |
| #10623910 | 2 |
| C3×#6716 | 2 |
| #10623805 | 2 |
| #10623802 | 2 |
| D3×C3⋊#168 | 2 |
| C2×#6716 | 3 |
| D3×#687 | 3 |
| D3×#214 | 5 |