Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 106 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×C4×Dic20 | C2 | semidirect |
| 4. C4×C3⋊#672 | C2 | semidirect |
| 5. #11745943 | C2 | semidirect |
| 6. #11745897 | C2 | semidirect |
| 20. #90941 | C4 | direct (N × H) |
| 24. C4×Dic20 | D3 | semidirect |
| 43. C3×Dic20 | C2×C4 | semidirect |
| 45. C3⋊#672 | C2×C4 | semidirect |
| 107. Dic20 | C4×D3 | semidirect |
| 122. C3×C4×C5 | SD32 | semidirect |
| 197. C4×C5 | #828 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 227. C3×C4 | #3959 | semidirect |
| 254. C5 | C4×#828 | semidirect |
| 263. C4 | #90941 | direct (N × H) |
| 266. C3 | C4×#3959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D24 | 2 |
| C3×C4×Dic20 | 2 |
| C2×#90941 | 2 |
| C4×C3⋊#672 | 2 |
| #11745943 | 2 |
| #11745897 | 2 |
| #11745893 | 2 |
| C4×#3959 | 3 |
| C4×#828 | 5 |