Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
| 3. C2×#90941 | C2 | semidirect |
| 4. C4⋊(C3⋊#672) | C2 | semidirect |
| 5. #11745893 | C2 | semidirect |
| 20. C4×Dic20 | D3 | semidirect |
| 37. C3×Dic20 | D4 | semidirect |
| 94. Dic20 | D12 | semidirect |
| 106. C3×C4×C5 | SD32 | semidirect |
| 176. C4×C5 | #828 | semidirect |
| 197. C3×C5 | #2207 | semidirect |
| 205. C3×C4 | #3959 | semidirect |
| 231. C5 | #70914 | semidirect |
| 239. C4 | #90941 | semidirect |
| 242. C3 | #10602087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4695 | 2 |
| C3×C4×Dic20 | 2 |
| C2×#90941 | 2 |
| C4⋊(C3⋊#672) | 2 |
| #11745893 | 2 |
| #10602087 | 3 |
| #70914 | 5 |