Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
300 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 144 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×#170 | C2 | semidirect |
| 3. C3×C22⋊#170 | C3 | direct (N × H) |
| 11. C2×C3×#170 | C2×C3 | semidirect |
| 14. C22×C32×C5 | C8 | semidirect |
| 18. C22⋊#170 | C32 | direct (N × H) |
| 32. C2×#170 | C2×C32 | semidirect |
| 40. C22×C3×C5 | C3×C8 | semidirect |
| 46. C32×C5 | C22⋊C8 | semidirect |
| 54. C22×C32 | #170 | semidirect |
| 70. C22×C5 | C32×C8 | semidirect |
| 80. C3×C5 | C3×C22⋊C8 | semidirect |
| 83. C22×C3 | C3×#170 | semidirect |
| 91. C32 | C22⋊#170 | direct (N × H) |
| 101. C5 | C32×C22⋊C8 | semidirect |
| 104. C22 | C32×#170 | semidirect |
| 108. C3 | C3×C22⋊#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Dic5 | 2 |
| C2×C32×#170 | 2 |
| C3×C22⋊#170 | 3 |
| C32×C22⋊C8 | 5 |