Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 82 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×#65193 | C2 | semidirect |
| 2. C2×C3×D80 | C2 | semidirect |
| 3. C3×C5×M64 | C2 | semidirect |
| 4. C3×#64669 | C2 | semidirect |
| 5. C3×D160 | C2 | semidirect |
| 6. #10600166 | C3 | direct (N × H) |
| 10. C3×Dic40 | C22 | semidirect |
| 14. C3×D80 | C22 | semidirect |
| 15. C3×C5×C32 | C22 | semidirect |
| 17. #65193 | C2×C3 | semidirect |
| 18. C2×D80 | C2×C3 | semidirect |
| 19. C5×M64 | C2×C3 | semidirect |
| 20. #64669 | C2×C3 | semidirect |
| 21. D160 | C2×C3 | semidirect |
| 36. C3×M64 | D5 | semidirect |
| 40. Dic40 | C22×C3 | semidirect |
| 44. D80 | C22×C3 | semidirect |
| 45. C5×C32 | C22×C3 | semidirect |
| 65. C3×C32 | C2×D5 | semidirect |
| 80. M64 | C3×D5 | semidirect |
| 116. C32 | C2×C3×D5 | semidirect |
| 148. C3×C5 | #2263 | semidirect |
| 174. C5 | C3×#2263 | semidirect |
| 182. C3 | #10600166 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65193 | 2 |
| C2×C3×D80 | 2 |
| C3×C5×M64 | 2 |
| C3×#64669 | 2 |
| C3×D160 | 2 |
| #10600166 | 3 |
| C3×#2263 | 5 |