Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 57. C3⋊#168 | Q16 | semidirect |
| 149. C3×C5 | #1707 | semidirect |
| 172. C5 | #71296 | semidirect |
| 179. C3 | #10602153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4682 | 2 |
| C3×#64988 | 2 |
| #11746947 | 2 |
| #11746923 | 2 |
| C8×C3⋊#168 | 2 |
| #10602153 | 3 |
| #71296 | 5 |