Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. C3×#66056 | C2 | semidirect |
| 4. C3×C5×#333 | C2 | semidirect |
| 5. C3×#64704 | C2 | semidirect |
| 6. #10599297 | C3 | direct (N × H) |
| 19. #66056 | C2×C3 | semidirect |
| 22. C5×#333 | C2×C3 | semidirect |
| 23. #64704 | C2×C3 | semidirect |
| 43. C3×#333 | D5 | semidirect |
| 69. C3×Dic10 | SD16 | semidirect |
| 102. #333 | C3×D5 | semidirect |
| 141. Dic10 | C3×SD16 | semidirect |
| 198. C3×C5 | #1623 | semidirect |
| 229. C5 | C3×#1623 | semidirect |
| 239. C3 | #10599297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66056 | 2 |
| C3×#65374 | 2 |
| C3×#65137 | 2 |
| C3×C5×#333 | 2 |
| C3×#64704 | 2 |
| #10599297 | 3 |
| C3×#1623 | 5 |