Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
212 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 23 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. C22⋊#4380 | C2 | semidirect |
| 4. C22×C5×C3⋊D3 | C4 | semidirect |
| 6. C2×C32×Dic5 | C4 | semidirect |
| 31. C22×C3⋊D3 | AGL(1,𝔽5) | semidirect |
| 42. C32×C5 | #99 | semidirect |
| 47. C2×Dic5 | #157 | semidirect |
| 88. C32 | #4011 | semidirect |
| 98. C5 | #63774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67140 | 2 |
| C22⋊#4380 | 2 |
| #63774 | 5 |
| #4011 | 9 |