Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 94 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×#66091 | C2 | semidirect |
| 2. C2×C3×#3958 | C2 | semidirect |
| 3. C3×#65197 | C2 | semidirect |
| 4. C3×#65186 | C2 | semidirect |
| 5. C3×C5×#361 | C2 | semidirect |
| 6. C3×#64735 | C2 | semidirect |
| 7. C3×#64717 | C2 | semidirect |
| 8. #10600051 | C3 | direct (N × H) |
| 17. C2×C3×D40 | C22 | semidirect |
| 19. C3×C5×M32 | C22 | semidirect |
| 20. C3×C5×#108 | C22 | semidirect |
| 23. C2×C3×#672 | C22 | semidirect |
| 27. #66091 | C2×C3 | semidirect |
| 28. C2×#3958 | C2×C3 | semidirect |
| 29. #65197 | C2×C3 | semidirect |
| 30. #65186 | C2×C3 | semidirect |
| 31. C5×#361 | C2×C3 | semidirect |
| 32. #64735 | C2×C3 | semidirect |
| 33. #64717 | C2×C3 | semidirect |
| 65. C3×#361 | D5 | semidirect |
| 76. C2×D40 | C22×C3 | semidirect |
| 78. C5×M32 | C22×C3 | semidirect |
| 79. C5×#108 | C22×C3 | semidirect |
| 82. C2×#672 | C22×C3 | semidirect |
| 122. C3×M32 | C2×D5 | semidirect |
| 124. C3×#108 | C2×D5 | semidirect |
| 157. #361 | C3×D5 | semidirect |
| 235. M32 | C2×C3×D5 | semidirect |
| 237. #108 | C2×C3×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | C3×#2192 | semidirect |
| 368. C3 | #10600051 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66091 | 2 |
| C2×C3×#3958 | 2 |
| C3×#65197 | 2 |
| C3×#65186 | 2 |
| C3×C5×#361 | 2 |
| C3×#64735 | 2 |
| C3×#64717 | 2 |
| #10600051 | 3 |
| C3×#2192 | 5 |