Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
212 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 70 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×#65208 | C2 | semidirect |
| 2. C3×#65201 | C2 | semidirect |
| 3. C3×C5×SD64 | C2 | semidirect |
| 4. C3×#64742 | C2 | semidirect |
| 5. C3×#64739 | C2 | semidirect |
| 6. C3×#64669 | C2 | semidirect |
| 7. C3×D5×C32 | C2 | semidirect |
| 8. #10600172 | C3 | direct (N × H) |
| 21. #65208 | C2×C3 | semidirect |
| 22. #65201 | C2×C3 | semidirect |
| 23. C5×SD64 | C2×C3 | semidirect |
| 24. #64742 | C2×C3 | semidirect |
| 25. #64739 | C2×C3 | semidirect |
| 26. #64669 | C2×C3 | semidirect |
| 27. D5×C32 | C2×C3 | semidirect |
| 43. C3×SD64 | D5 | semidirect |
| 95. SD64 | C3×D5 | semidirect |
| 171. C3×C5 | #2262 | semidirect |
| 198. C5 | C3×#2262 | semidirect |
| 206. C3 | #10600172 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65208 | 2 |
| C3×#65201 | 2 |
| C3×C5×SD64 | 2 |
| C3×#64742 | 2 |
| C3×#64739 | 2 |
| C3×#64669 | 2 |
| C3×D5×C32 | 2 |
| #10600172 | 3 |
| C3×#2262 | 5 |