Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 106 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×#66047 | C2 | semidirect |
| 3. C3×#65137 | C2 | semidirect |
| 4. C3×C5×#331 | C2 | semidirect |
| 5. C3×#64704 | C2 | semidirect |
| 6. #10599195 | C3 | direct (N × H) |
| 19. #66047 | C2×C3 | semidirect |
| 21. #65137 | C2×C3 | semidirect |
| 22. C5×#331 | C2×C3 | semidirect |
| 23. #64704 | C2×C3 | semidirect |
| 43. C3×#331 | D5 | semidirect |
| 104. #331 | C3×D5 | semidirect |
| 207. C3×C5 | #1620 | semidirect |
| 243. C5 | C3×#1620 | semidirect |
| 254. C3 | #10599195 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66047 | 2 |
| C3×#65362 | 2 |
| C3×#65137 | 2 |
| C3×C5×#331 | 2 |
| C3×#64704 | 2 |
| #10599195 | 3 |
| C3×#1620 | 5 |