Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
260 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 8. #10600128 | C3 | direct (N × H) |
| 40. C3×Dic20 | Q8 | semidirect |
| 98. Dic20 | C3×Q8 | semidirect |
| 196. C3×C5 | #2227 | semidirect |
| 225. C5 | C3×#2227 | semidirect |
| 235. C3 | #10600128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65163 | 2 |
| C3×#65162 | 2 |
| C3×C5×#366 | 2 |
| C3×#64723 | 2 |
| C3×#64721 | 2 |
| C3×#64712 | 2 |
| C3×#64709 | 2 |
| #10600128 | 3 |
| C3×#2227 | 5 |