Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 340 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×#65377 | C2 | semidirect |
| 2. C3×#65373 | C2 | semidirect |
| 4. C3×#65127 | C2 | semidirect |
| 5. C3×C5×#333 | C2 | semidirect |
| 6. C3×#64705 | C2 | semidirect |
| 7. C3×#64699 | C2 | semidirect |
| 8. #10599295 | C3 | direct (N × H) |
| 25. #65377 | C2×C3 | semidirect |
| 26. #65373 | C2×C3 | semidirect |
| 28. #65127 | C2×C3 | semidirect |
| 29. C5×#333 | C2×C3 | semidirect |
| 30. #64705 | C2×C3 | semidirect |
| 31. #64699 | C2×C3 | semidirect |
| 55. C3×#333 | D5 | semidirect |
| 133. #333 | C3×D5 | semidirect |
| 263. C3×C5 | #1697 | semidirect |
| 310. C5 | C3×#1697 | semidirect |
| 325. C3 | #10599295 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65377 | 2 |
| C3×#65373 | 2 |
| C3×#65132 | 2 |
| C3×#65127 | 2 |
| C3×C5×#333 | 2 |
| C3×#64705 | 2 |
| C3×#64699 | 2 |
| #10599295 | 3 |
| C3×#1697 | 5 |