Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
264 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 3. #11746325 | C2 | semidirect |
| 5. C3×#64723 | C2 | semidirect |
| 6. #11745944 | C2 | semidirect |
| 7. #11745898 | C2 | semidirect |
| 27. #64723 | D3 | semidirect |
| 212. C3×C5 | #2237 | semidirect |
| 246. C5 | #69214 | semidirect |
| 258. C3 | #10599893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11747952 | 2 |
| #11747682 | 2 |
| #11746325 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C3×#64723 | 2 |
| #11745944 | 2 |
| #11745898 | 2 |
| #10599893 | 3 |
| #69214 | 5 |