Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11746945 | C2 | semidirect |
| 4. #11746866 | C2 | semidirect |
| 6. #11745868 | C2 | semidirect |
| 7. #11745860 | C2 | semidirect |
| 91. C3⋊#168 | SD16 | semidirect |
| 259. C3×C5 | #1686 | semidirect |
| 301. C5 | #68412 | semidirect |
| 314. C3 | #10601817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751177 | 2 |
| C5×#5075 | 2 |
| #11746945 | 2 |
| #11746866 | 2 |
| C3×#64764 | 2 |
| #11745868 | 2 |
| #11745860 | 2 |
| #10601817 | 3 |
| #68412 | 5 |