Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 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. #11750782 | C2 | semidirect |
| 4. #11746941 | C2 | semidirect |
| 5. #11746929 | C2 | semidirect |
| 7. C3×C8×#168 | C2 | semidirect |
| 29. C8×#168 | D3 | semidirect |
| 224. C3×C5 | #1708 | semidirect |
| 259. C5 | #68059 | semidirect |
| 270. C3 | #10601974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750782 | 2 |
| C5×#4694 | 2 |
| #11747066 | 2 |
| #11746941 | 2 |
| #11746929 | 2 |
| #11746906 | 2 |
| C3×C8×#168 | 2 |
| #10601974 | 3 |
| #68059 | 5 |