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×#65444 | C2 | semidirect |
| 3. C2×C3×#3932 | C2 | semidirect |
| 4. C3×#65161 | C2 | semidirect |
| 5. C3×C5×#357 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 7. C3×#64712 | C2 | semidirect |
| 8. #10599996 | C3 | direct (N × H) |
| 23. #65444 | C2×C3 | semidirect |
| 25. C2×#3932 | C2×C3 | semidirect |
| 26. #65161 | C2×C3 | semidirect |
| 27. C5×#357 | C2×C3 | semidirect |
| 28. #64721 | C2×C3 | semidirect |
| 29. #64712 | C2×C3 | semidirect |
| 56. C3×#357 | D5 | semidirect |
| 127. #357 | C3×D5 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | C3×#2210 | semidirect |
| 301. C3 | #10599996 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65444 | 2 |
| C2×C3×#3958 | 2 |
| C2×C3×#3932 | 2 |
| C3×#65161 | 2 |
| C3×C5×#357 | 2 |
| C3×#64721 | 2 |
| C3×#64712 | 2 |
| #10599996 | 3 |
| C3×#2210 | 5 |