Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 6. #10602171 | C3 | direct (N × H) |
| 176. C3×C5 | #1676 | semidirect |
| 205. C5 | C3×#1676 | semidirect |
| 215. C3 | #10602171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C3×#65380 | 2 |
| C3×C8×Dic10 | 2 |
| C3×#64766 | 2 |
| C3×#64678 | 2 |
| #10602171 | 3 |
| C3×#1676 | 5 |