Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 208 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 |
|---|---|---|
| 2. C3×D5×Q32 | C2 | semidirect |
| 3. C3×C5×Q64 | C2 | semidirect |
| 4. C3×#64742 | C2 | semidirect |
| 5. C3×#64741 | C2 | semidirect |
| 6. C3×#64669 | C2 | semidirect |
| 7. C3×#64667 | C2 | semidirect |
| 8. #10600177 | C3 | direct (N × H) |
| 22. D5×Q32 | C2×C3 | semidirect |
| 23. C5×Q64 | C2×C3 | semidirect |
| 24. #64742 | C2×C3 | semidirect |
| 25. #64741 | C2×C3 | semidirect |
| 26. #64669 | C2×C3 | semidirect |
| 27. #64667 | C2×C3 | semidirect |
| 42. C3×Q64 | D5 | semidirect |
| 94. Q64 | C3×D5 | semidirect |
| 170. C3×C5 | #2264 | semidirect |
| 195. C5 | C3×#2264 | semidirect |
| 203. C3 | #10600177 | 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×D5×Q32 | 2 |
| C3×C5×Q64 | 2 |
| C3×#64742 | 2 |
| C3×#64741 | 2 |
| C3×#64669 | 2 |
| C3×#64667 | 2 |
| #10600177 | 3 |
| C3×#2264 | 5 |