Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 124 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×C3⋊#170 | C2 | semidirect |
| 3. C2×C32×#170 | C2 | semidirect |
| 4. C3×#6738 | C2 | direct (N × H) |
| 6. C2×#6738 | C3 | direct (N × H) |
| 12. C3×C3⋊#170 | C22 | semidirect |
| 13. C32×#170 | C22 | semidirect |
| 17. C2×C3⋊#170 | C2×C3 | semidirect |
| 20. C2×C3×#170 | D3 | semidirect |
| 21. C2×C3×#170 | C2×C3 | semidirect |
| 23. #6738 | C2×C3 | direct (N × H) |
| 25. C2×C3×D15 | C8 | semidirect |
| 46. C3⋊#170 | C22×C3 | semidirect |
| 49. C3×#170 | C2×D3 | semidirect |
| 50. C3×#170 | C22×C3 | semidirect |
| 53. C2×C32×C5 | C2×C8 | semidirect |
| 55. C3×D15 | C2×C8 | semidirect |
| 58. C2×#170 | C3×D3 | semidirect |
| 70. C2×D15 | C3×C8 | semidirect |
| 91. C32×C5 | C22×C8 | semidirect |
| 98. #170 | C2×C3×D3 | semidirect |
| 108. C2×C3×C5 | D3×C8 | semidirect |
| 109. C2×C3×C5 | C2×C3×C8 | semidirect |
| 112. D15 | C2×C3×C8 | semidirect |
| 136. C2×C32 | D5⋊C8 | semidirect |
| 144. C3×C5 | C2×D3×C8 | semidirect |
| 145. C3×C5 | C22×C3×C8 | semidirect |
| 161. C2×C5 | C3×D3×C8 | semidirect |
| 164. C32 | C2×D5⋊C8 | semidirect |
| 175. C2×C3 | #6738 | direct (N × H) |
| 176. C2×C3 | C3×D5⋊C8 | semidirect |
| 180. C5 | C2×C3×D3×C8 | semidirect |
| 188. C3 | C2×#6738 | direct (N × H) |
| 189. C3 | C2×C3×D5⋊C8 | semidirect |
| 191. C2 | C3×#6738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1200 | 2 |
| C2×C3×C3⋊#170 | 2 |
| C2×C32×#170 | 2 |
| C3×#6738 | 2 |
| C2×C3×D5⋊C8 | 3 |
| C2×#6738 | 3 |
| C2×C3×D3×C8 | 5 |