Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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×#67126 | C2 | semidirect |
| 12. C22×C32×C5 | C8 | semidirect |
| 41. C32×C5 | C22⋊C8 | semidirect |
| 49. C22×C32 | #168 | semidirect |
| 64. C22×C5 | #622 | semidirect |
| 85. C32 | C22⋊#168 | semidirect |
| 95. C5 | C22⋊#622 | semidirect |
| 98. C22 | #67126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C2×#67126 | 2 |
| C22⋊#622 | 5 |
| C22⋊#168 | 9 |