Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 98 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×#65470 | C2 | semidirect |
| 5. C3×C5×#358 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 7. C3×#64712 | C2 | semidirect |
| 8. #10600027 | C3 | direct (N × H) |
| 23. #65470 | C2×C3 | semidirect |
| 27. C5×#358 | C2×C3 | semidirect |
| 28. #64721 | C2×C3 | semidirect |
| 29. #64712 | C2×C3 | semidirect |
| 56. C3×#358 | D5 | semidirect |
| 127. #358 | C3×D5 | semidirect |
| 138. C3×Dic5 | SD32 | semidirect |
| 220. Dic5 | C3×SD32 | semidirect |
| 241. C3×C5 | #2208 | semidirect |
| 278. C5 | C3×#2208 | semidirect |
| 290. C3 | #10600027 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65470 | 2 |
| C2×C3×#3960 | 2 |
| C2×C3×#3932 | 2 |
| C3×#65161 | 2 |
| C3×C5×#358 | 2 |
| C3×#64721 | 2 |
| C3×#64712 | 2 |
| #10600027 | 3 |
| C3×#2208 | 5 |