Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 1. C3×#66087 | C2 | semidirect |
| 2. C3×#65431 | C2 | semidirect |
| 3. C3×#65197 | C2 | semidirect |
| 4. C2×C3×#3932 | C2 | semidirect |
| 5. C3×C5×#350 | C2 | semidirect |
| 6. C3×#64737 | C2 | semidirect |
| 7. C3×#64730 | C2 | semidirect |
| 8. #10599920 | C3 | direct (N × H) |
| 27. #66087 | C2×C3 | semidirect |
| 28. #65431 | C2×C3 | semidirect |
| 29. #65197 | C2×C3 | semidirect |
| 30. C2×#3932 | C2×C3 | semidirect |
| 31. C5×#350 | C2×C3 | semidirect |
| 32. #64737 | C2×C3 | semidirect |
| 33. #64730 | C2×C3 | semidirect |
| 67. C3×#350 | D5 | semidirect |
| 159. #350 | C3×D5 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | C3×#2193 | semidirect |
| 357. C3 | #10599920 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66087 | 2 |
| C3×#65431 | 2 |
| C3×#65197 | 2 |
| C2×C3×#3932 | 2 |
| C3×C5×#350 | 2 |
| C3×#64737 | 2 |
| C3×#64730 | 2 |
| #10599920 | 3 |
| C3×#2193 | 5 |