Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 110 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. C2×C3×Dic30 | C2 | semidirect |
| 3. C3×#6716 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊#168 | C2 | semidirect |
| 5. C2×#6716 | C3 | direct (N × H) |
| 13. C3×Dic30 | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 19. C2×Dic30 | C2×C3 | semidirect |
| 21. #6716 | C2×C3 | direct (N × H) |
| 22. C2×C3⋊#168 | C2×C3 | semidirect |
| 50. Dic30 | C22×C3 | semidirect |
| 54. C3⋊#168 | C22×C3 | semidirect |
| 59. C2×C32×C5 | SD16 | semidirect |
| 99. C32×C5 | C2×SD16 | semidirect |
| 120. C2×C3×C5 | #214 | semidirect |
| 121. C2×C3×C5 | C3×SD16 | semidirect |
| 151. C2×C32 | #687 | semidirect |
| 158. C3×C5 | C2×#214 | semidirect |
| 159. C3×C5 | C2×C3×SD16 | semidirect |
| 178. C2×C5 | C3×#214 | semidirect |
| 180. C32 | C2×#687 | semidirect |
| 194. C2×C3 | C3×#687 | semidirect |
| 195. C2×C3 | #6716 | direct (N × H) |
| 198. C5 | C2×C3×#214 | semidirect |
| 206. C3 | C2×C3×#687 | semidirect |
| 207. C3 | C2×#6716 | direct (N × H) |
| 209. C2 | C3×#6716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C3×Dic30 | 2 |
| C3×#6716 | 2 |
| C2×C3×C3⋊#168 | 2 |
| C2×#6716 | 3 |
| C2×C3×#687 | 3 |
| C2×C3×#214 | 5 |