Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
400 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 4. #10599510 | C3 | direct (N × H) |
| 8. C3×#3947 | C4 | semidirect |
| 9. C3×C8×Dic5 | C4 | semidirect |
| 28. #3947 | C3×C4 | semidirect |
| 29. C8×Dic5 | C3×C4 | semidirect |
| 101. C3×C5 | #1747 | semidirect |
| 118. C5 | C3×#1747 | semidirect |
| 124. C3 | #10599510 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65411 | 2 |
| C3×C5×#338 | 2 |
| C3×#64777 | 2 |
| #10599510 | 3 |
| C3×#1747 | 5 |