Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 92 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×#65732 | C2 | semidirect |
| 3. C3×#64905 | C2 | semidirect |
| 4. C3×#64852 | C2 | semidirect |
| 5. C3×#64844 | C2 | semidirect |
| 6. #10604123 | C3 | direct (N × H) |
| 13. C3×C5×D16 | C4 | semidirect |
| 14. C3×#3959 | C4 | semidirect |
| 15. C3×Dic40 | C4 | semidirect |
| 18. #65732 | C2×C3 | semidirect |
| 20. #64905 | C2×C3 | semidirect |
| 21. #64852 | C2×C3 | semidirect |
| 22. #64844 | C2×C3 | semidirect |
| 47. C5×D16 | C3×C4 | semidirect |
| 48. #3959 | C3×C4 | semidirect |
| 49. Dic40 | C3×C4 | semidirect |
| 66. C3×D16 | AGL(1,𝔽5) | semidirect |
| 123. D16 | C3×AGL(1,𝔽5) | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | C3×#2179 | semidirect |
| 191. C3 | #10604123 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65732 | 2 |
| C3×#65201 | 2 |
| C3×#64905 | 2 |
| C3×#64852 | 2 |
| C3×#64844 | 2 |
| #10604123 | 3 |
| C3×#2179 | 5 |