Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. #11751179 | C2 | semidirect |
| 5. C3×#64767 | C2 | semidirect |
| 6. #11745868 | C2 | semidirect |
| 7. #11745859 | C2 | semidirect |
| 29. #64767 | D3 | semidirect |
| 90. C3⋊#168 | SD16 | semidirect |
| 256. C3×C5 | #1673 | semidirect |
| 297. C5 | #68443 | semidirect |
| 310. C3 | #10601830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751179 | 2 |
| C5×#5083 | 2 |
| #11747077 | 2 |
| #11746998 | 2 |
| C3×#64767 | 2 |
| #11745868 | 2 |
| #11745859 | 2 |
| #10601830 | 3 |
| #68443 | 5 |