Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11751253 | C2 | semidirect |
| 3. #11748071 | C2 | semidirect |
| 4. C5×#4563 | C2 | semidirect |
| 5. #11745934 | C2 | semidirect |
| 6. #11745910 | C2 | semidirect |
| 7. #11745878 | C2 | semidirect |
| 18. C3×#3959 | C4 | semidirect |
| 19. C3×#3958 | C4 | semidirect |
| 41. C3×Dic20 | C2×C4 | semidirect |
| 42. C3×D40 | C2×C4 | semidirect |
| 46. C3×#672 | C2×C4 | semidirect |
| 52. #4563 | D5 | semidirect |
| 62. #3959 | Dic3 | semidirect |
| 63. #3958 | Dic3 | semidirect |
| 108. Dic20 | C2×Dic3 | semidirect |
| 109. D40 | C2×Dic3 | semidirect |
| 114. #672 | C2×Dic3 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #71515 | semidirect |
| 270. C3 | #10600047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751253 | 2 |
| C3×#65436 | 2 |
| #11748071 | 2 |
| C5×#4563 | 2 |
| #11745934 | 2 |
| #11745910 | 2 |
| #11745878 | 2 |
| #10600047 | 3 |
| #71515 | 5 |