Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 82 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×#66069 | C2 | semidirect |
| 2. C3×#65384 | C2 | semidirect |
| 4. C3×#65041 | C2 | semidirect |
| 5. C3×C5×#356 | C2 | semidirect |
| 6. C3×#64698 | C2 | semidirect |
| 7. C3×#64697 | C2 | semidirect |
| 8. #10599960 | C3 | direct (N × H) |
| 29. #66069 | C2×C3 | semidirect |
| 30. #65384 | C2×C3 | semidirect |
| 32. #65041 | C2×C3 | semidirect |
| 33. C5×#356 | C2×C3 | semidirect |
| 34. #64698 | C2×C3 | semidirect |
| 35. #64697 | C2×C3 | semidirect |
| 76. C3×#356 | D5 | semidirect |
| 184. #356 | C3×D5 | semidirect |
| 359. C3×C5 | #2203 | semidirect |
| 408. C5 | C3×#2203 | semidirect |
| 422. C3 | #10599960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66069 | 2 |
| C3×#65384 | 2 |
| C3×#65042 | 2 |
| C3×#65041 | 2 |
| C3×C5×#356 | 2 |
| C3×#64698 | 2 |
| C3×#64697 | 2 |
| #10599960 | 3 |
| C3×#2203 | 5 |