Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 6. #10604841 | C3 | direct (N × H) |
| 61. C3×#170 | Q16 | semidirect |
| 121. #170 | C3×Q16 | semidirect |
| 170. C3×C5 | #1591 | semidirect |
| 198. C5 | C3×#1591 | semidirect |
| 207. C3 | #10604841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65788 | 2 |
| C3×Q16×Dic5 | 2 |
| C3×Q8⋊#170 | 2 |
| C3×#64882 | 2 |
| C3×C8×#170 | 2 |
| #10604841 | 3 |
| C3×#1591 | 5 |