Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
880 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 236 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×D120 | C2 | semidirect |
| 2. C22×C5×D24 | C2 | semidirect |
| 3. C22×C3×#672 | C2 | semidirect |
| 4. C2×#90939 | C2 | direct (N × H) |
| 10. C2×D120 | C22 | semidirect |
| 12. C2×C5×D24 | C22 | semidirect |
| 13. C2×C3×#672 | C22 | semidirect |
| 14. #90939 | C22 | direct (N × H) |
| 19. C22×#672 | D3 | semidirect |
| 30. D120 | C23 | semidirect |
| 32. C5×D24 | C23 | semidirect |
| 33. C3×#672 | C23 | semidirect |
| 35. C22×D24 | D5 | semidirect |
| 46. C2×#672 | C2×D3 | semidirect |
| 67. C2×D24 | C2×D5 | semidirect |
| 83. #672 | C22×D3 | semidirect |
| 88. C22×C3×C5 | D16 | semidirect |
| 108. D24 | C22×D5 | semidirect |
| 132. C2×C3×C5 | C2×D16 | semidirect |
| 151. C22×C5 | D48 | semidirect |
| 171. C3×C5 | C22×D16 | semidirect |
| 172. C22×C3 | #3958 | semidirect |
| 181. C2×C5 | C2×D48 | semidirect |
| 197. C2×C3 | C2×#3958 | semidirect |
| 201. C5 | C22×D48 | semidirect |
| 206. C22 | #90939 | direct (N × H) |
| 210. C3 | C22×#3958 | semidirect |
| 213. C2 | C2×#90939 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D120 | 2 |
| C22×C5×D24 | 2 |
| C22×C3×#672 | 2 |
| C2×#90939 | 2 |
| C22×#3958 | 3 |
| C22×D48 | 5 |