Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 94 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×#65480 | C2 | semidirect |
| 2. C2×C3×#3960 | C2 | semidirect |
| 4. C3×#65161 | C2 | semidirect |
| 5. C3×C5×#358 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 7. C3×#64711 | C2 | semidirect |
| 8. #10600028 | C3 | direct (N × H) |
| 23. #65480 | C2×C3 | semidirect |
| 24. C2×#3960 | C2×C3 | semidirect |
| 26. #65161 | C2×C3 | semidirect |
| 27. C5×#358 | C2×C3 | semidirect |
| 28. #64721 | C2×C3 | semidirect |
| 29. #64711 | C2×C3 | semidirect |
| 55. C3×#358 | D5 | semidirect |
| 126. #358 | C3×D5 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | C3×#2210 | semidirect |
| 301. C3 | #10600028 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65480 | 2 |
| C2×C3×#3960 | 2 |
| C2×C3×D80 | 2 |
| C3×#65161 | 2 |
| C3×C5×#358 | 2 |
| C3×#64721 | 2 |
| C3×#64711 | 2 |
| #10600028 | 3 |
| C3×#2210 | 5 |