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 |
|---|---|---|
| 2. C3×#65183 | C2 | semidirect |
| 3. C3×#65158 | C2 | semidirect |
| 4. C3×C5×#365 | C2 | semidirect |
| 5. C3×#64732 | C2 | semidirect |
| 6. C3×#64715 | C2 | semidirect |
| 7. C3×#64708 | C2 | semidirect |
| 8. #10600103 | C3 | direct (N × H) |
| 20. C3×#3932 | C4 | semidirect |
| 21. C3×D80 | C4 | semidirect |
| 24. #65183 | C2×C3 | semidirect |
| 25. #65158 | C2×C3 | semidirect |
| 26. C5×#365 | C2×C3 | semidirect |
| 27. #64732 | C2×C3 | semidirect |
| 28. #64715 | C2×C3 | semidirect |
| 29. #64708 | C2×C3 | semidirect |
| 39. C3×Dic20 | C2×C4 | semidirect |
| 42. C3×D40 | C2×C4 | semidirect |
| 46. C3×C5×C16 | C2×C4 | semidirect |
| 51. C3×#365 | D5 | semidirect |
| 66. #3932 | C3×C4 | semidirect |
| 67. D80 | C3×C4 | semidirect |
| 106. Dic20 | C2×C3×C4 | semidirect |
| 109. D40 | C2×C3×C4 | semidirect |
| 113. C5×C16 | C2×C3×C4 | semidirect |
| 118. #365 | C3×D5 | semidirect |
| 149. C3×C16 | C4×D5 | semidirect |
| 224. C16 | C3×C4×D5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | C3×AGL(1,ℤ/16) | semidirect |
| 270. C3 | #10600103 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65197 | 2 |
| C3×#65183 | 2 |
| C3×#65158 | 2 |
| C3×C5×#365 | 2 |
| C3×#64732 | 2 |
| C3×#64715 | 2 |
| C3×#64708 | 2 |
| #10600103 | 3 |
| C3×AGL(1,ℤ/16) | 5 |