Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 320 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 |
|---|---|---|
| 1. #11751181 | C2 | semidirect |
| 5. C3×#64767 | C2 | semidirect |
| 6. #11745868 | C2 | semidirect |
| 7. #11745863 | C2 | semidirect |
| 29. #64767 | D3 | semidirect |
| 88. C3⋊#168 | SD16 | semidirect |
| 249. C3×C5 | #1691 | semidirect |
| 289. C5 | #68450 | semidirect |
| 302. C3 | #10601833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751181 | 2 |
| C5×#5083 | 2 |
| #11747014 | 2 |
| #11746883 | 2 |
| C3×#64767 | 2 |
| #11745868 | 2 |
| #11745863 | 2 |
| #10601833 | 3 |
| #68450 | 5 |