Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 104 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×C32×Dic10 | C2 | semidirect |
| 3. C2×C3×C3⋊#168 | C2 | semidirect |
| 4. C3×#6656 | C2 | direct (N × H) |
| 6. C2×#6656 | C3 | direct (N × H) |
| 13. C32×Dic10 | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 19. C2×C3×Dic10 | D3 | semidirect |
| 20. C2×C3×Dic10 | C2×C3 | semidirect |
| 21. C2×C3⋊#168 | C2×C3 | semidirect |
| 24. #6656 | C2×C3 | direct (N × H) |
| 52. C3×Dic10 | C2×D3 | semidirect |
| 53. C3×Dic10 | C22×C3 | semidirect |
| 54. C3⋊#168 | C22×C3 | semidirect |
| 58. C2×C32×C5 | SD16 | semidirect |
| 62. C2×Dic10 | C3×D3 | semidirect |
| 98. C32×C5 | C2×SD16 | semidirect |
| 105. Dic10 | C2×C3×D3 | semidirect |
| 117. C2×C3×C5 | #215 | semidirect |
| 118. C2×C3×C5 | C3×SD16 | semidirect |
| 148. C2×C32 | #687 | semidirect |
| 156. C3×C5 | C2×#215 | semidirect |
| 157. C3×C5 | C2×C3×SD16 | semidirect |
| 175. C2×C5 | C3×#215 | semidirect |
| 177. C32 | C2×#687 | semidirect |
| 189. C2×C3 | #6656 | direct (N × H) |
| 190. C2×C3 | C3×#687 | semidirect |
| 194. C5 | C2×C3×#215 | semidirect |
| 202. C3 | C2×#6656 | direct (N × H) |
| 203. C3 | C2×C3×#687 | semidirect |
| 205. C2 | C3×#6656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D12 | 2 |
| C2×C32×Dic10 | 2 |
| C2×C3×C3⋊#168 | 2 |
| C3×#6656 | 2 |
| C2×C3×#687 | 3 |
| C2×#6656 | 3 |
| C2×C3×#215 | 5 |