Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
222 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
| 5. (C2×D3)⋊#170 | C3 | direct (N × H) |
| 16. C2×C3⋊#170 | C2×C3 | semidirect |
| 19. C2×C3×#170 | D3 | semidirect |
| 20. C2×C3×#170 | C2×C3 | semidirect |
| 24. C2×C3×C5×D3 | C8 | semidirect |
| 56. C2×#170 | C3×D3 | semidirect |
| 72. C2×C5×D3 | C3×C8 | semidirect |
| 88. C32×C5 | C22⋊C8 | semidirect |
| 99. C2×C3×D3 | #170 | semidirect |
| 146. C3×C5 | (C2×D3)⋊C8 | semidirect |
| 147. C3×C5 | C3×C22⋊C8 | semidirect |
| 156. C2×D3 | C3×#170 | semidirect |
| 169. C32 | C22⋊#170 | semidirect |
| 188. C5 | C3×(C2×D3)⋊C8 | semidirect |
| 197. C3 | (C2×D3)⋊#170 | direct (N × H) |
| 198. C3 | C3×C22⋊#170 | semidirect |
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×C32×#170 | 2 |
| C3×C22⋊#170 | 3 |
| (C2×D3)⋊#170 | 3 |
| C3×(C2×D3)⋊C8 | 5 |