Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. C3×C5×#467 | C2 | semidirect |
| 3. C2×C3×#3960 | C2 | semidirect |
| 4. C3×C22⋊#672 | C2 | semidirect |
| 5. C3×#64711 | C2 | semidirect |
| 6. #10601878 | C3 | direct (N × H) |
| 8. C2×C3×C5×Q16 | C22 | semidirect |
| 14. C3×C5×#107 | C22 | semidirect |
| 17. C2×C3×#672 | C22 | semidirect |
| 20. C5×#467 | C2×C3 | semidirect |
| 21. C2×#3960 | C2×C3 | semidirect |
| 22. C22⋊#672 | C2×C3 | semidirect |
| 23. #64711 | C2×C3 | semidirect |
| 44. C3×#467 | D5 | semidirect |
| 48. C2×C5×Q16 | C22×C3 | semidirect |
| 54. C5×#107 | C22×C3 | semidirect |
| 57. C2×#672 | C22×C3 | semidirect |
| 78. C2×C3×Q16 | C2×D5 | semidirect |
| 86. C3×#107 | C2×D5 | semidirect |
| 108. #467 | C3×D5 | semidirect |
| 113. C22×C3×C5 | SD32 | semidirect |
| 161. C2×Q16 | C2×C3×D5 | semidirect |
| 169. #107 | C2×C3×D5 | semidirect |
| 196. C22×C5 | C3×SD32 | semidirect |
| 225. C3×C5 | #2187 | semidirect |
| 232. C22×C3 | #3960 | semidirect |
| 267. C5 | C3×#2187 | semidirect |
| 274. C22 | C3×#3960 | semidirect |
| 281. C3 | #10601878 | 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×C5×#467 | 2 |
| C2×C3×#3960 | 2 |
| C3×C22⋊#672 | 2 |
| C3×#64711 | 2 |
| #10601878 | 3 |
| C3×#2187 | 5 |