Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
300 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
| 14. C22×C32×C5 | C8 | semidirect |
| 40. C22×C3×C5 | C3⋊C8 | semidirect |
| 46. C32×C5 | C22⋊C8 | semidirect |
| 54. C22×C32 | #170 | semidirect |
| 70. C22×C5 | C3⋊(C3⋊C8) | semidirect |
| 80. C3×C5 | #830 | semidirect |
| 83. C22×C3 | C3⋊#170 | semidirect |
| 91. C32 | C22⋊#170 | semidirect |
| 101. C5 | #63657 | semidirect |
| 104. C22 | C3⋊(C3⋊#170) | semidirect |
| 108. C3 | #91241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Dic5 | 2 |
| C2×C3⋊(C3⋊#170) | 2 |
| #91241 | 3 |
| #63657 | 5 |