Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 90 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×#66017 | C2 | semidirect |
| 2. C3×#65347 | C2 | semidirect |
| 3. C3×#65001 | C2 | semidirect |
| 4. C3×C5×#329 | C2 | semidirect |
| 5. C3×#64684 | C2 | semidirect |
| 6. #10599143 | C3 | direct (N × H) |
| 17. C3×#4020 | C22 | semidirect |
| 18. C3×C5×#97 | C22 | semidirect |
| 19. C3×#3935 | C22 | semidirect |
| 21. #66017 | C2×C3 | semidirect |
| 22. #65347 | C2×C3 | semidirect |
| 23. #65001 | C2×C3 | semidirect |
| 24. C5×#329 | C2×C3 | semidirect |
| 25. #64684 | C2×C3 | semidirect |
| 52. C3×#329 | D5 | semidirect |
| 63. #4020 | C22×C3 | semidirect |
| 64. C5×#97 | C22×C3 | semidirect |
| 65. #3935 | C22×C3 | semidirect |
| 100. C3×#97 | C2×D5 | semidirect |
| 127. #329 | C3×D5 | semidirect |
| 196. #97 | C2×C3×D5 | semidirect |
| 258. C3×C5 | #1655 | semidirect |
| 303. C5 | C3×#1655 | semidirect |
| 317. C3 | #10599143 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66017 | 2 |
| C3×#65347 | 2 |
| C3×#65001 | 2 |
| C3×C5×#329 | 2 |
| C3×#64684 | 2 |
| #10599143 | 3 |
| C3×#1655 | 5 |