Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11752384 | C2 | semidirect |
| 2. #11751742 | C2 | semidirect |
| 4. C3×#64898 | C2 | semidirect |
| 5. #11746564 | C2 | semidirect |
| 6. #11746553 | C2 | semidirect |
| 7. #11746541 | C2 | semidirect |
| 29. #64898 | D3 | semidirect |
| 240. C3×C5 | #2170 | semidirect |
| 273. C5 | #69122 | semidirect |
| 282. C3 | #10604083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752384 | 2 |
| #11751742 | 2 |
| #11748207 | 2 |
| C3×#64898 | 2 |
| #11746564 | 2 |
| #11746553 | 2 |
| #11746541 | 2 |
| #10604083 | 3 |
| #69122 | 5 |