Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 114 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×#64989 | C2 | semidirect |
| 3. C3×C5×#346 | C2 | semidirect |
| 4. C3×#64730 | C2 | semidirect |
| 5. C3×#64726 | C2 | semidirect |
| 6. #10599878 | C3 | direct (N × H) |
| 14. C3×Dic40 | C4 | semidirect |
| 15. C3×#3932 | C4 | semidirect |
| 16. C3×D80 | C4 | semidirect |
| 19. #64989 | C2×C3 | semidirect |
| 20. C5×#346 | C2×C3 | semidirect |
| 21. #64730 | C2×C3 | semidirect |
| 22. #64726 | C2×C3 | semidirect |
| 40. C3×#346 | D5 | semidirect |
| 48. Dic40 | C3×C4 | semidirect |
| 49. #3932 | C3×C4 | semidirect |
| 50. D80 | C3×C4 | semidirect |
| 89. #346 | C3×D5 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | C3×#2179 | semidirect |
| 191. C3 | #10599878 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65193 | 2 |
| C3×#64989 | 2 |
| C3×C5×#346 | 2 |
| C3×#64730 | 2 |
| C3×#64726 | 2 |
| #10599878 | 3 |
| C3×#2179 | 5 |