Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 76 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. #11751156 | C2 | semidirect |
| 3. #11747098 | C2 | semidirect |
| 4. #11746909 | C2 | semidirect |
| 5. C3×#64760 | C2 | semidirect |
| 6. #11745847 | C2 | semidirect |
| 7. #11745847 | C2 | semidirect |
| 10. #91758 | C22 | semidirect |
| 23. #91087 | C22 | semidirect |
| 24. C3×#3935 | C22 | semidirect |
| 25. C3×#3935 | C22 | semidirect |
| 35. #64760 | D3 | semidirect |
| 89. #3935 | C2×D3 | semidirect |
| 90. #3935 | C2×D3 | semidirect |
| 347. C3×C5 | #1659 | semidirect |
| 405. C5 | #68352 | semidirect |
| 424. C3 | #10602742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5683 | 2 |
| #11751156 | 2 |
| #11747098 | 2 |
| #11746909 | 2 |
| C3×#64760 | 2 |
| #11745847 | 2 |
| #10602742 | 3 |
| #68352 | 5 |