Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 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×#64762 | C2 | semidirect |
| 3. C3×#64761 | C2 | semidirect |
| 4. #10598288 | C3 | direct (N × H) |
| 7. C3×C5×#127 | C4 | semidirect |
| 9. C3×C5×#97 | C4 | semidirect |
| 14. #64762 | C2×C3 | semidirect |
| 15. #64761 | C2×C3 | semidirect |
| 32. C5×#127 | C3×C4 | semidirect |
| 34. C5×#97 | C3×C4 | semidirect |
| 53. C3×#127 | Dic5 | semidirect |
| 57. C3×#97 | Dic5 | semidirect |
| 107. #127 | C3×Dic5 | semidirect |
| 111. #97 | C3×Dic5 | semidirect |
| 149. C3×C5 | #1406 | semidirect |
| 180. C5 | C3×#1406 | semidirect |
| 190. C3 | #10598288 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#496 | 2 |
| C3×#64762 | 2 |
| C3×#64761 | 2 |
| #10598288 | 3 |
| C3×#1406 | 5 |