Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
628 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 114 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×C5×#492 | C2 | semidirect |
| 3. C3×#65373 | C2 | semidirect |
| 4. C3×#64764 | C2 | semidirect |
| 5. C3×#64679 | C2 | semidirect |
| 6. #10602059 | C3 | direct (N × H) |
| 9. C3×C5×C4⋊Q8 | C22 | semidirect |
| 14. C3×C4×C5×C8 | C22 | semidirect |
| 17. C3×C4⋊#168 | C22 | semidirect |
| 20. C5×#492 | C2×C3 | semidirect |
| 21. #65373 | C2×C3 | semidirect |
| 22. #64764 | C2×C3 | semidirect |
| 23. #64679 | C2×C3 | semidirect |
| 42. C3×#492 | D5 | semidirect |
| 48. C5×C4⋊Q8 | C22×C3 | semidirect |
| 53. C4×C5×C8 | C22×C3 | semidirect |
| 56. C4⋊#168 | C22×C3 | semidirect |
| 72. C3×D20 | SD16 | semidirect |
| 79. C3×C4⋊Q8 | C2×D5 | semidirect |
| 87. C3×C4×C8 | C2×D5 | semidirect |
| 106. #492 | C3×D5 | semidirect |
| 153. D20 | C3×SD16 | semidirect |
| 160. C4⋊Q8 | C2×C3×D5 | semidirect |
| 168. C4×C8 | C2×C3×D5 | semidirect |
| 221. C3×C5 | #1629 | semidirect |
| 261. C5 | C3×#1629 | semidirect |
| 274. C3 | #10602059 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66051 | 2 |
| C3×C5×#492 | 2 |
| C3×#65373 | 2 |
| C3×#64764 | 2 |
| C3×#64679 | 2 |
| #10602059 | 3 |
| C3×#1629 | 5 |