Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11751122 | C2 | semidirect |
| 3. #11746930 | C2 | semidirect |
| 5. C3×Q8⋊#168 | C2 | semidirect |
| 6. #11745857 | C2 | semidirect |
| 32. Q8⋊#168 | D3 | semidirect |
| 297. C3×C5 | #1637 | semidirect |
| 343. C5 | #68269 | semidirect |
| 358. C3 | #10602708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×D12 | 2 |
| #11751122 | 2 |
| #11746930 | 2 |
| #11746883 | 2 |
| C3×Q8⋊#168 | 2 |
| #11745857 | 2 |
| #11745837 | 2 |
| #10602708 | 3 |
| #68269 | 5 |