Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 33. C3×Dic20 | C8 | semidirect |
| 82. Dic20 | C3⋊C8 | semidirect |
| 161. C3×C5 | #1579 | semidirect |
| 187. C5 | #70902 | semidirect |
| 195. C3 | #10599310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic20 | 2 |
| #11746846 | 2 |
| #11746276 | 2 |
| C5×#4457 | 2 |
| #11745840 | 2 |
| #10599310 | 3 |
| #70902 | 5 |