Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 87. C3×#168 | Q16 | semidirect |
| 171. #168 | #216 | semidirect |
| 234. C3×C5 | #1692 | semidirect |
| 268. C5 | #70963 | semidirect |
| 279. C3 | #10599305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65120 | 2 |
| #11747095 | 2 |
| #11746954 | 2 |
| #11746941 | 2 |
| #11746307 | 2 |
| C5×#4481 | 2 |
| #11745867 | 2 |
| #10599305 | 3 |
| #70963 | 5 |