Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 2. C2×#91113 | C2 | semidirect |
| 4. C2×C3×#3961 | C2 | semidirect |
| 5. #11745902 | C2 | semidirect |
| 6. #11745897 | C2 | semidirect |
| 28. C2×#3961 | D3 | semidirect |
| 148. C2×C5×D3 | Q32 | semidirect |
| 274. C3×C5 | #2188 | semidirect |
| 278. C2×D3 | #3961 | semidirect |
| 314. C5 | #71502 | semidirect |
| 326. C3 | #10601880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic20 | 2 |
| C2×#91113 | 2 |
| C5×#5188 | 2 |
| C2×C3×#3961 | 2 |
| #11745902 | 2 |
| #11745897 | 2 |
| (C2×D3)⋊#672 | 2 |
| #10601880 | 3 |
| #71502 | 5 |