Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×#65196 | C2 | semidirect |
| 3. #11747531 | C2 | semidirect |
| 4. #11746336 | C2 | semidirect |
| 5. C5×#4511 | C2 | semidirect |
| 6. #11745885 | C2 | semidirect |
| 7. #11745874 | C2 | semidirect |
| 26. #65196 | D3 | semidirect |
| 57. #4511 | D5 | semidirect |
| 240. C3×C5 | #2171 | semidirect |
| 273. C5 | #71453 | semidirect |
| 282. C3 | #10600094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65196 | 2 |
| #11748076 | 2 |
| #11747531 | 2 |
| #11746336 | 2 |
| C5×#4511 | 2 |
| #11745885 | 2 |
| #11745874 | 2 |
| #10600094 | 3 |
| #71453 | 5 |