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. #11751738 | C2 | semidirect |
| 3. #11746757 | C2 | semidirect |
| 4. C3×#64889 | C2 | semidirect |
| 5. #11746550 | C2 | semidirect |
| 21. #64889 | D3 | semidirect |
| 164. C3×C5 | #2171 | semidirect |
| 188. C5 | #69301 | semidirect |
| 195. C3 | #10604862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751738 | 2 |
| #11748062 | 2 |
| #11746757 | 2 |
| C3×#64889 | 2 |
| #11746550 | 2 |
| #10604862 | 3 |
| #69301 | 5 |