Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 126 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×C3×C3⋊#170 | C2 | semidirect |
| 4. D3×C3⋊#170 | C2 | direct (N × H) |
| 12. C3⋊(C3⋊#170) | C22 | semidirect |
| 13. C3×C3⋊#170 | C22 | semidirect |
| 21. C2×C3⋊#170 | D3 | direct (N × H) |
| 25. C2×C3×C5×D3 | C8 | semidirect |
| 49. C3⋊#170 | C2×D3 | direct (N × H) |
| 53. C2×C32×C5 | C2×C8 | semidirect |
| 55. C3×C5×D3 | C2×C8 | semidirect |
| 72. C2×C5×D3 | C3⋊C8 | semidirect |
| 91. C32×C5 | C22×C8 | semidirect |
| 100. C2×C3×D3 | #170 | semidirect |
| 109. C2×C3×C5 | D3×C8 | semidirect |
| 110. C2×C3×C5 | C2×C3⋊C8 | semidirect |
| 113. C5×D3 | C2×C3⋊C8 | semidirect |
| 136. C2×C32 | C2×#170 | semidirect |
| 138. C3×D3 | C2×#170 | semidirect |
| 144. C3×C5 | C2×D3×C8 | semidirect |
| 145. C3×C5 | C22×C3⋊C8 | semidirect |
| 151. C2×D3 | C3⋊#170 | direct (N × H) |
| 162. C2×C5 | D3×C3⋊C8 | semidirect |
| 164. C32 | C22×#170 | semidirect |
| 175. C2×C3 | D3×#170 | semidirect |
| 176. C2×C3 | C2×C3⋊#170 | semidirect |
| 179. D3 | C2×C3⋊#170 | direct (N × H) |
| 180. C5 | C2×D3×C3⋊C8 | semidirect |
| 188. C3 | C2×D3×#170 | semidirect |
| 189. C3 | C22×C3⋊#170 | semidirect |
| 191. C2 | D3×C3⋊#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Dic5 | 2 |
| C2×C3⋊(C3⋊#170) | 2 |
| C2×C3×C3⋊#170 | 2 |
| D3×C3⋊#170 | 2 |
| C22×C3⋊#170 | 3 |
| C2×D3×#170 | 3 |
| C2×D3×C3⋊C8 | 5 |