Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 2. C3×#64860 | C2 | semidirect |
| 3. #10598746 | C3 | direct (N × H) |
| 11. #64860 | C2×C3 | semidirect |
| 96. C3×C5 | #1355 | semidirect |
| 116. C5 | C3×#1355 | semidirect |
| 123. C3 | #10598746 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65360 | 2 |
| C3×#64860 | 2 |
| #10598746 | 3 |
| C3×#1355 | 5 |