Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 102 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×#65441 | C2 | semidirect |
| 3. C3×#65183 | C2 | semidirect |
| 4. C3×C5×#361 | C2 | semidirect |
| 5. C3×#64738 | C2 | semidirect |
| 6. C3×#64732 | C2 | semidirect |
| 7. C3×#64714 | C2 | semidirect |
| 8. #10600047 | C3 | direct (N × H) |
| 16. C3×#3959 | C4 | semidirect |
| 17. C3×#3958 | C4 | semidirect |
| 23. #65441 | C2×C3 | semidirect |
| 25. #65183 | C2×C3 | semidirect |
| 26. C5×#361 | C2×C3 | semidirect |
| 27. #64738 | C2×C3 | semidirect |
| 28. #64732 | C2×C3 | semidirect |
| 29. #64714 | C2×C3 | semidirect |
| 41. C3×Dic20 | C2×C4 | semidirect |
| 42. C3×D40 | C2×C4 | semidirect |
| 47. C3×#672 | C2×C4 | semidirect |
| 52. C3×#361 | D5 | semidirect |
| 62. #3959 | C3×C4 | semidirect |
| 63. #3958 | C3×C4 | semidirect |
| 108. Dic20 | C2×C3×C4 | semidirect |
| 109. D40 | C2×C3×C4 | semidirect |
| 114. #672 | C2×C3×C4 | semidirect |
| 119. #361 | C3×D5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | C3×AGL(1,ℤ/16) | semidirect |
| 270. C3 | #10600047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65441 | 2 |
| C3×#65436 | 2 |
| C3×#65183 | 2 |
| C3×C5×#361 | 2 |
| C3×#64738 | 2 |
| C3×#64732 | 2 |
| C3×#64714 | 2 |
| #10600047 | 3 |
| C3×AGL(1,ℤ/16) | 5 |