Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. #11747531 | C2 | semidirect |
| 3. C5×#4463 | C2 | semidirect |
| 4. C3×#64681 | C2 | semidirect |
| 5. #11745890 | C2 | semidirect |
| 22. #64681 | D3 | semidirect |
| 40. #4463 | D5 | semidirect |
| 164. C3×C5 | #2171 | semidirect |
| 188. C5 | #69076 | semidirect |
| 195. C3 | #10600094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750801 | 2 |
| #11747531 | 2 |
| C5×#4463 | 2 |
| C3×#64681 | 2 |
| #11745890 | 2 |
| #10600094 | 3 |
| #69076 | 5 |