Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 90 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×#66018 | C2 | semidirect |
| 2. C3×#65347 | C2 | semidirect |
| 3. C3×#65002 | C2 | semidirect |
| 4. C3×#65001 | C2 | semidirect |
| 5. C3×C5×#329 | C2 | semidirect |
| 6. C3×#64685 | C2 | semidirect |
| 7. C3×#64684 | C2 | semidirect |
| 8. #10599144 | C3 | direct (N × H) |
| 29. #66018 | C2×C3 | semidirect |
| 30. #65347 | C2×C3 | semidirect |
| 31. #65002 | C2×C3 | semidirect |
| 32. #65001 | C2×C3 | semidirect |
| 33. C5×#329 | C2×C3 | semidirect |
| 34. #64685 | C2×C3 | semidirect |
| 35. #64684 | C2×C3 | semidirect |
| 73. C3×#329 | D5 | semidirect |
| 176. #329 | C3×D5 | semidirect |
| 350. C3×C5 | #1656 | semidirect |
| 406. C5 | C3×#1656 | semidirect |
| 424. C3 | #10599144 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66018 | 2 |
| C3×#65347 | 2 |
| C3×#65002 | 2 |
| C3×#65001 | 2 |
| C3×C5×#329 | 2 |
| C3×#64685 | 2 |
| C3×#64684 | 2 |
| #10599144 | 3 |
| C3×#1656 | 5 |