Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×C3×D40 | C2 | semidirect |
| 2. C3×#65404 | C2 | semidirect |
| 3. C2×C3×D80 | C2 | semidirect |
| 4. C3×C5×C22⋊C16 | C2 | semidirect |
| 5. C3×#64729 | C2 | semidirect |
| 6. #10599901 | C3 | direct (N × H) |
| 13. C2×C3×D40 | C22 | semidirect |
| 14. C2×C3×C5×C16 | C22 | semidirect |
| 16. C3×#3950 | C22 | semidirect |
| 19. C22×D40 | C2×C3 | semidirect |
| 20. #65404 | C2×C3 | semidirect |
| 21. C2×D80 | C2×C3 | semidirect |
| 22. C5×C22⋊C16 | C2×C3 | semidirect |
| 23. #64729 | C2×C3 | semidirect |
| 40. C3×D40 | D4 | semidirect |
| 46. C3×C22⋊C16 | D5 | semidirect |
| 53. C2×D40 | C22×C3 | semidirect |
| 54. C2×C5×C16 | C22×C3 | semidirect |
| 56. #3950 | C22×C3 | semidirect |
| 86. C2×C3×C16 | C2×D5 | semidirect |
| 105. D40 | C3×D4 | semidirect |
| 111. C22⋊C16 | C3×D5 | semidirect |
| 114. C22×C3×C5 | D16 | semidirect |
| 172. C2×C16 | C2×C3×D5 | semidirect |
| 202. C22×C5 | C3×D16 | semidirect |
| 233. C3×C5 | #2184 | semidirect |
| 243. C22×C3 | D80 | semidirect |
| 280. C5 | C3×#2184 | semidirect |
| 290. C22 | C3×D80 | semidirect |
| 296. C3 | #10599901 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D40 | 2 |
| C3×#65404 | 2 |
| C2×C3×D80 | 2 |
| C3×C5×C22⋊C16 | 2 |
| C3×#64729 | 2 |
| #10599901 | 3 |
| C3×#2184 | 5 |