Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 110 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×#65040 | C2 | semidirect |
| 3. C3×C5×#355 | C2 | semidirect |
| 4. C3×#64762 | C2 | semidirect |
| 5. C3×#64698 | C2 | semidirect |
| 6. #10599958 | C3 | direct (N × H) |
| 22. #65040 | C2×C3 | semidirect |
| 23. C5×#355 | C2×C3 | semidirect |
| 24. #64762 | C2×C3 | semidirect |
| 25. #64698 | C2×C3 | semidirect |
| 55. C3×#355 | D5 | semidirect |
| 137. #355 | C3×D5 | semidirect |
| 284. C3×C5 | #2132 | semidirect |
| 334. C5 | C3×#2132 | semidirect |
| 349. C3 | #10599958 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66002 | 2 |
| C3×#65040 | 2 |
| C3×C5×#355 | 2 |
| C3×#64762 | 2 |
| C3×#64698 | 2 |
| #10599958 | 3 |
| C3×#2132 | 5 |