Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 100 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 | #1672 | semidirect |
| 268. C5 | #70943 | semidirect |
| 279. C3 | #10601845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751122 | 2 |
| C5×#5031 | 2 |
| C3×Q8×#168 | 2 |
| #11746941 | 2 |
| #11745864 | 2 |
| #11745863 | 2 |
| #11745857 | 2 |
| #10601845 | 3 |
| #70943 | 5 |