Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 90 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. #11751008 | C2 | semidirect |
| 3. #11747525 | C2 | semidirect |
| 4. C5×#4511 | C2 | semidirect |
| 5. C3×#64735 | C2 | semidirect |
| 6. #11745890 | C2 | semidirect |
| 7. #11745874 | C2 | semidirect |
| 30. #64735 | D3 | semidirect |
| 56. #4511 | D5 | semidirect |
| 240. C3×C5 | #2171 | semidirect |
| 273. C5 | #69123 | semidirect |
| 282. C3 | #10600094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751008 | 2 |
| #11748076 | 2 |
| #11747525 | 2 |
| C5×#4511 | 2 |
| C3×#64735 | 2 |
| #11745890 | 2 |
| #11745874 | 2 |
| #10600094 | 3 |
| #69123 | 5 |